Prof. Natalia Kopteva
Biography
I am a Professor at the Department of Mathematics and Statistics at the University of Limerick, Ireland. I hold an M.Sc. in Applied Mathematics and a Ph.D. in Computational Mathematics from Moscow State University. In the past, I held academic positions at Moscow State University, University College Cork, and University of Strathclyde. I am ASSOCIATED with INAF - Irish Numerical Analysis Forum, of which I am one of the organisers, and which includes online seminars in all areas of numerical analysis, MACSI - Mathematics Applications Consortium for Science and Industry, and SFI Centre for Research Training in Foundations of Data Science.For my more comprehensive profile, please visit
https://natalia-kopteva.github.io/home/ See also my profiles at Google Scholar + ResearchGate + arXiv + ORCID (identifier 0000-0001-7477-6926).
Research Interests
Numerical Analysis for partial differential equations: a posteriori error estimation, finite element and finite difference methods, singularly perturbed differential equations, semilinear reaction-diffusion, convection-dominated convection-diffusion problems, time-fractional parabolic equations (subdiffusion equations), layer-adapted anisotropic meshes.Professional Activities
Education
- 1997 Moscow State University - Ph.D.
- 1993 Moscow State University, - M.Sc.
Peer Reviewed Journals
Pointwise-in-time a posteriori error control for higher-order discretizations of time-fractional parabolic equations
Franz S.;Kopteva N. (2023) Pointwise-in-time a posteriori error control for higher-order discretizations of time-fractional parabolic equations. Journal Of Computational And Applied Mathematics
POINTWISE A POSTERIORI ERROR ESTIMATES FOR DISCONTINUOUS GALERKIN METHODS FOR SINGULARLY PERTURBED REACTION-DIFFUSION EQUATIONS<sup>*</sup>
Kopteva N.;Rankin R. (2023) POINTWISE A POSTERIORI ERROR ESTIMATES FOR DISCONTINUOUS GALERKIN METHODS FOR SINGULARLY PERTURBED REACTION-DIFFUSION EQUATIONS<sup>*</sup>. Siam Journal On Numerical Analysis :1938-1961
Maximum principle for time-fractional parabolic equations with a reaction coefficient of arbitrary sign
Kopteva N. (2022) Maximum principle for time-fractional parabolic equations with a reaction coefficient of arbitrary sign. Applied Mathematics Letters
Pointwise-in-time a posteriori error control for time-fractional parabolic equations
Kopteva, N (2022) Pointwise-in-time a posteriori error control for time-fractional parabolic equations. OXFORD : PERGAMON-ELSEVIER SCIENCE LTD Applied Mathematics Letters
A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations
Kopteva N.;Stynes M. (2022) A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations. Journal Of Scientific Computing
ERROR ANALYSIS OF AN L2-TYPE METHOD ON GRADED MESHES FOR A FRACTIONAL-ORDER PARABOLIC PROBLEM
Kopteva, N (2021) ERROR ANALYSIS OF AN L2-TYPE METHOD ON GRADED MESHES FOR A FRACTIONAL-ORDER PARABOLIC PROBLEM. PROVIDENCE : AMER MATHEMATICAL SOC Mathematics Of Computation :19-40
ERROR ANALYSIS FOR TIME-FRACTIONAL SEMILINEAR PARABOLIC EQUATIONS USING UPPER AND LOWER SOLUTIONS
Kopteva, N (2020) ERROR ANALYSIS FOR TIME-FRACTIONAL SEMILINEAR PARABOLIC EQUATIONS USING UPPER AND LOWER SOLUTIONS. PHILADELPHIA : SIAM PUBLICATIONS Siam Journal On Numerical Analysis :2212-2234
Lower a posteriori error estimates on anisotropic meshes
Kopteva N. (2020) Lower a posteriori error estimates on anisotropic meshes. Numerische Mathematik
How accurate are finite elements on anisotropic triangulations in the maximum norm?
Kopteva N. (2020) How accurate are finite elements on anisotropic triangulations in the maximum norm?. Journal Of Computational And Applied Mathematics
Error analysis for a fractional-derivative parabolic problem on quasi-graded meshes using barrier functions
Kopteva N.;Meng X. (2020) Error analysis for a fractional-derivative parabolic problem on quasi-graded meshes using barrier functions. Siam Journal On Numerical Analysis :1217-1238
Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions
Kopteva N. (2019) Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions. Mathematics Of Computation :2135-2155
Logarithm cannot be removed in maximum norm error estimates for linear finite elements in 3D
Kopteva N. (2018) Logarithm cannot be removed in maximum norm error estimates for linear finite elements in 3D. Mathematics Of Computation :1527-1532
Improved maximum-norm a posteriori error estimates for linear and semilinear parabolic equations
Kopteva, N,Linss, T (2017) Improved maximum-norm a posteriori error estimates for linear and semilinear parabolic equations. Advances In Computational Mathematics :999-1022
Energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes
Kopteva, N (2017) Energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes. Numerische Mathematik :607-642
Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem
Kopteva, N,Stynes, M (2017) Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem. Advances In Computational Mathematics :77-99
Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems
Demlow, A,Kopteva, N (2016) Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems. Numerische Mathematik :707-742
Maximum-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes
Kopteva, N (2015) Maximum-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes. Siam Journal On Numerical Analysis :2519-2544
An efficient collocation method for a Caputo two-point boundary value problem
Kopteva, N,Stynes, M (2015) An efficient collocation method for a Caputo two-point boundary value problem. Bit Numerical Mathematics :1105-1123
Linear finite elements may be only first-order pointwise accurate on anisotropic triangulations
Kopteva N. (2014) Linear finite elements may be only first-order pointwise accurate on anisotropic triangulations. Mathematics Of Computation :2061-2070
Linear finite elements may be only first-order pointwise accurate on anisotropic triangulations
Kopteva, N (2014) Linear finite elements may be only first-order pointwise accurate on anisotropic triangulations. Mathematics Of Computation :2061-2070
Maximum norm a posteriori error estimation for parabolic problems using elliptic reconstructions
Kopteva, N,Linss, T (2013) Maximum norm a posteriori error estimation for parabolic problems using elliptic reconstructions. Siam Journal On Numerical Analysis :1494-1524
A second-order overlapping Schwarz method for a 2d singularly perturbed semilinear reaction-diffusion problem
Kopteva, N,Pickett, M (2012) A second-order overlapping Schwarz method for a 2d singularly perturbed semilinear reaction-diffusion problem. Mathematics Of Computation :81-105
Maximum norm a posteriori error estimation for a time-dependent reaction-diffusion problem
Kopteva N.;Linß T. (2012) Maximum norm a posteriori error estimation for a time-dependent reaction-diffusion problem. Computational Methods In Applied Mathematics :189-205
Green's function estimates for a singularly perturbed convection-diffusion problem
Franz, S; Kopteva, N (2012) Green's function estimates for a singularly perturbed convection-diffusion problem. Journal Of Differential Equations :1521-1545
Maximum norm a posteriori error estimate for a 3d singularly perturbed semilinear reaction-diffusion problem
Chadha, NM; Kopteva, N (2011) Maximum norm a posteriori error estimate for a 3d singularly perturbed semilinear reaction-diffusion problem. Advances In Computational Mathematics :33-55
Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem
Kopteva, N; Stynes, M (2011) Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem. Numerische Mathematik :787-810
Pointwise error estimates for a singularly perturbed time-dependent semilinear reaction-diffusion problem
Kopteva, N; Savescu, SB (2011) Pointwise error estimates for a singularly perturbed time-dependent semilinear reaction-diffusion problem. Ima Journal Of Numerical Analysis :616-639
A robust grid equidistribution method for a one-dimensional singularly perturbed semilinear reaction-diffusion problem
Chadha, NM; Kopteva, N (2011) A robust grid equidistribution method for a one-dimensional singularly perturbed semilinear reaction-diffusion problem. Ima Journal Of Numerical Analysis :188-211
Shishkin meshes in the numerical solution of singularly perturbed differential equations
Kopteva, N; O'Riordan, E (2010) Shishkin meshes in the numerical solution of singularly perturbed differential equations. International Journal Of Numerical Analysis And Modeling :393-415
A POSTERIORI ERROR ESTIMATION FOR A DEFECT-CORRECTION METHOD APPLIED TO CONVECTION-DIFFUSION PROBLEMS
Linss, T; Kopteva, N (2010) A POSTERIORI ERROR ESTIMATION FOR A DEFECT-CORRECTION METHOD APPLIED TO CONVECTION-DIFFUSION PROBLEMS. International Journal Of Numerical Analysis And Modeling :718-733
A posteriori error estimation for a defect-correction method applied to convection-diffusion problems
Linss T.;Kopteva N. (2010) A posteriori error estimation for a defect-correction method applied to convection-diffusion problems. International Journal Of Numerical Analysis And Modeling :718-733
A singularly perturbed semilinear reaction-diffusion problem in a polygonal domain
Kellogg, RB; Kopteva, N (2010) A singularly perturbed semilinear reaction-diffusion problem in a polygonal domain. Journal Of Differential Equations :184-208
A robust overlapping Schwarz method for a singularly perturbed semilinear reaction-diffusion problem with multiple solutions
Kopteva N.;Pickett M.;Purtill H. (2009) A robust overlapping Schwarz method for a singularly perturbed semilinear reaction-diffusion problem with multiple solutions. International Journal Of Numerical Analysis And Modeling :680-695
Pointwise error estimates for a singularly perturbed time-dependent semilinear reaction-diffusion problem
Kopteva, N; Savescu, SB (2009) Pointwise error estimates for a singularly perturbed time-dependent semilinear reaction-diffusion problem. Ima Journal Of Numerical Analysis
Numerical analysis of a 2d singularly perturbed semilinear reaction-diffusion problem
Kopteva, N (2009) Numerical analysis of a 2d singularly perturbed semilinear reaction-diffusion problem. Lecture Notes In Computer Science :80-91
A robust grid equidistribution method for a 1d singularly perturbed semilinear reaction-diffusion problem
Chadha, NM; Kopteva, N (2009) A robust grid equidistribution method for a 1d singularly perturbed semilinear reaction-diffusion problem. Ima Journal Of Numerical Analysis
A ROBUST OVERLAPPING SCHWARZ METHOD FOR SINGULARLY PERTURBED SEMILINEAR REACTION-DIFFUSION PROBLEM WITH MULTIPLE SOLUTIONS
Kopteva, N; Pickett, M; Purtill, H (2009) A ROBUST OVERLAPPING SCHWARZ METHOD FOR SINGULARLY PERTURBED SEMILINEAR REACTION-DIFFUSION PROBLEM WITH MULTIPLE SOLUTIONS. International Journal Of Numerical Analysis And Modeling :680-695
A robust overlapping Schwarz method for a singularly perturbed semilinear reaction-diffusion problem with multiple solutions
Kopteva N., Pickett M., Purtill H. (2009) A robust overlapping Schwarz method for a singularly perturbed semilinear reaction-diffusion problem with multiple solutions. International Journal Of Numerical Analysis And Modeling :680-695
Steady rimming flows with surface tension
Benilov, ES; Benilov, MS; Kopteva, N (2008) Steady rimming flows with surface tension. Journal Of Fluid Mechanics :91-118
Pointwise approximation of corner singularities for a singularly perturbed reaction-diffusion equation in an L-shaped domain
Andreev, VB; Kopteva, N (2008) Pointwise approximation of corner singularities for a singularly perturbed reaction-diffusion equation in an L-shaped domain. Mathematics Of Computation :2125-2139
Maximum norm a posteriori error estimate for a 2D singularly perturbed semilinear reaction-diffusion problem
Kopteva, N (2008) Maximum norm a posteriori error estimate for a 2D singularly perturbed semilinear reaction-diffusion problem. Siam Journal On Numerical Analysis :1602-1618
Maximum norm a posteriori error estimates for a ID singularly perturbed semilinear reaction-diffusion problem
Kopteva, N (2007) Maximum norm a posteriori error estimates for a ID singularly perturbed semilinear reaction-diffusion problem. Ima Journal Of Numerical Analysis :576-592
Maximum norm error analysis of a 2D singularly perturbed semilinear reaction-diffusion problem
Kopteva, N (2007) Maximum norm error analysis of a 2D singularly perturbed semilinear reaction-diffusion problem. Mathematics Of Computation :631-646
Numerical analysis of singularly perturbed nonlinear reaction-diffusion problems with multiple solutions
Stynes, M; Kopteva, N (2006) Numerical analysis of singularly perturbed nonlinear reaction-diffusion problems with multiple solutions. Computers & Mathematics With Applications :857-864
The formation of river channels
Fowler, AC; Kopteva, N; Oakley, C (2006) The formation of river channels. Siam Journal On Applied Mathematics :1016-1040
Grid equidistribution for reaction-diffusion problems in one dimension
Kopteva, N; Madden, N; Stynes, M (2005) Grid equidistribution for reaction-diffusion problems in one dimension. Numerical Algorithms :305-322
Does surface tension stabilize liquid films inside a rotating horizontal cylinder?
Benilov, ES; Kopteva, N; O'Brien, SBG (2005) Does surface tension stabilize liquid films inside a rotating horizontal cylinder?. Quarterly Journal Of Mechanics And Applied Mathematics :185-200
How accurate is the streamline-diffusion FEM inside characteristic (boundary and interior) layers?
Kopteva, N (2004) How accurate is the streamline-diffusion FEM inside characteristic (boundary and interior) layers?. Computer Methods In Applied Mechanics And Engineering :4875-4889
Numerical analysis of a singularly perturbed nonlinear reaction-diffusion problem with multiple solutions
Kopteva, N; Stynes, M (2004) Numerical analysis of a singularly perturbed nonlinear reaction-diffusion problem with multiple solutions. Applied Numerical Mathematics :273-288
Error expansion for an upwind scheme applied to a two-dimensional convection-diffusion problem
Kopteva, N (2003) Error expansion for an upwind scheme applied to a two-dimensional convection-diffusion problem. Siam J. Numer. Anal. :1851-1869
Uniform second order pointwise convergence of a central difference approximation for a quasilinear convection-diffusion problem
Kopteva, N; Linss, T (2001) Uniform second order pointwise convergence of a central difference approximation for a quasilinear convection-diffusion problem. Journal Of Computational And Applied Mathematics :257-267
Approximation of derivatives in a convection-diffusion two-point boundary value problem,
Kopteva, N; Stynes, M (2001) Approximation of derivatives in a convection-diffusion two-point boundary value problem,. Applied Numerical Mathematics :47-60
A robust adaptive method for a quasilinear one-dimensional convection-diffusion problem
Kopteva, N; Stynes, M (2001) A robust adaptive method for a quasilinear one-dimensional convection-diffusion problem. Siam J. Numer. Anal. :1446-1467
Uniform pointwise convergence of difference schemes for convection-diffusion problems on layer-adapted meshes
Kopteva, N (2001) Uniform pointwise convergence of difference schemes for convection-diffusion problems on layer-adapted meshes. Computing :179-197
Maximum norm a posteriori error estimates for a one-dimensional convection-diffusion problem
Kopteva, N (2001) Maximum norm a posteriori error estimates for a one-dimensional convection-diffusion problem. Siam J. Numer. Anal. :423-441
On the convergence, uniform with respect to the small parameter, of a scheme with central difference on refined grids, (Russian)
Kopteva, N (1999) On the convergence, uniform with respect to the small parameter, of a scheme with central difference on refined grids, (Russian). Zh. Vychisl. Mat. Mat. Fiz. :1662-1678
On the convergence, uniform with respect to the small parameter, of a scheme with central difference on refined grids
Kopteva, N (1999) On the convergence, uniform with respect to the small parameter, of a scheme with central difference on refined grids. Comput.Math. Math. Phys. :1594-1610
The two-dimensional Sobolev inequality in the case of an arbitrary grid
Kopteva, N (1998) The two-dimensional Sobolev inequality in the case of an arbitrary grid. Zh. Vychisl. Mat. Mat. Fiz. :596-599
On the convergence, uniform with respect to a small parameter, of a scheme with weights for a one-dimensional nonstationary convection-diffusion equation
Kopteva, N (1997) On the convergence, uniform with respect to a small parameter, of a scheme with weights for a one-dimensional nonstationary convection-diffusion equation. Zh. Vychisl. Mat. Mat. Fiz. :1213-1220
On the convergence, uniform with respect to a small parameter, of a four-point scheme for a one-dimensional stationary convection-diffusion equation
Kopteva, N (1997) On the convergence, uniform with respect to a small parameter, of a four-point scheme for a one-dimensional stationary convection-diffusion equation. Differential Equations :958-964
On the convergence, uniform with respect to the small parameter, of a difference scheme for an elliptic problem in a strip
Kopteva, N (1997) On the convergence, uniform with respect to the small parameter, of a difference scheme for an elliptic problem in a strip. Xv Vychisl. Mat. Kibernet :6-9
On the convergence, uniform with respect to a small parameter, of a four-point scheme for a one-dimensional stationary convection-diffusion equation, (Russian)
Kopteva, N (1996) On the convergence, uniform with respect to a small parameter, of a four-point scheme for a one-dimensional stationary convection-diffusion equation, (Russian). Differ. Uravn :951-957
Books
Book Chapters
Convergence theory of moving grid methods for singular perturbation problems
Kopteva, N (2007) Convergence theory of moving grid methods for singular perturbation problems. Beijing : Science Press Adaptive Computations: Theory and Algorithms :147-191
Edited Books
BAIL 2008 - Boundary and Interior Layers, Proceedings of the International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods, Limerick, July 2008, Lecture Notes in Computational Science and Engineering, 69
(2009) BAIL 2008 - Boundary and Interior Layers, Proceedings of the International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods, Limerick, July 2008, Lecture Notes in Computational Science and Engineering, 69. Berlin Heidelberg : Springer
Other Journals
Some asymptotic expansions for a semilinear reaction-diffusion problem in a sector
Kellogg, RB; Kopteva, N (2009) Some asymptotic expansions for a semilinear reaction-diffusion problem in a sector. arXiv:0902.0987
Conference Publications
Lecture Notes in Computational Science and Engineering
Kopteva N. (2020) Lecture Notes in Computational Science and Engineering. :143-156
Lecture Notes in Computational Science and Engineering
Kopteva N. (2017) Lecture Notes in Computational Science and Engineering. :141-154
NUMERICAL ANALYSIS AND ITS APPLICATIONS, NAA 2012
Kopteva, N,Linss, T,Dimov I,Farago I,Vulkov, L (2013) NUMERICAL ANALYSIS AND ITS APPLICATIONS, NAA 2012. Computer Safety, Reliability And Security :50-61
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Kopteva N.;Linß T. (2013) Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes In Computer Science (Including Subseries Lecture Notes In Artificial Intelligence And Lecture Notes In Bioinformatics) :50-61
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Kopteva N. (2009) Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes In Computer Science (Including Subseries Lecture Notes In Artificial Intelligence And Lecture Notes In Bioinformatics) :80-91
NUMERICAL ANALYSIS AND ITS APPLICATIONS
Kopteva, N (2009) NUMERICAL ANALYSIS AND ITS APPLICATIONS. Numerical Analysis And Its Applications :80-91
4th International Conference Finite Difference Methods: Theory and Applications,
N. Kopteva (2006) 4th International Conference Finite Difference Methods: Theory and Applications,. :105-114
10th International Conference Mathematical Modelling and Analysis and 2nd International Conference Computational Methods in Applied Mathematics
N.Kopteva (2005) 10th International Conference Mathematical Modelling and Analysis and 2nd International Conference Computational Methods in Applied Mathematics. :227-233
Numerical Methods for Problems with Layer Phenomena, 3rd Annual Workshop
N. Kopteva, N. Madden & M. Stynes (2004) Numerical Methods for Problems with Layer Phenomena, 3rd Annual Workshop. :46-51
Numerical Methods for Problems with Layer Phenomena, 3rd Annual Workshop
N. Kopteva & M. Stynes (2004) Numerical Methods for Problems with Layer Phenomena, 3rd Annual Workshop. :20-25
Analytical and Computational Methods for Convection-Dominated and Singularly Perturbed Problems
V. B. Andreev & N. V. Kopteva (2000) Analytical and Computational Methods for Convection-Dominated and Singularly Perturbed Problems. :133-139
Conference Contributions
Conference on Computational Methods in Applied Mathematics CMAM-3
N. Kopteva (2007) Conference on Computational Methods in Applied Mathematics CMAM-3.
Published Reports
Editorials
Book Reviews
Other Publications
Shishkin meshes in the numerical solution of singularly perturbed differential equations
Kopteva N.;O'Riordan E. (2010) Shishkin meshes in the numerical solution of singularly perturbed differential equations. International Journal Of Numerical Analysis And Modeling :393-415