### Biography

B.A. (Mathematics) Dublin University 1979 M.Sc., Dublin, 1982 Ph.D. Dublin, 1986

### Research Interests

Numerical solution of singular perturbation problems. Special mesh methods. Adaptive and moving mesh methods.

### Publications

#### 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

Hegarty, AF; Kopteva, N; O'Riordan, E; Stynes, M (Eds)

(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

(Ed.)
Berlin Heidelberg :
Springer
Berlin Heidelberg

Robust Computational Techniques for Boundary Layers

Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI

(2000)
Robust Computational Techniques for Boundary Layers

Boca raton, Florida :
Chapman & Hall/CRC
Boca raton, Florida

#### Book Chapters

Key to the computation of the transfer of a substance by convection-diffusion in a laminar fluid.

Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI

(1993)
Key to the computation of the transfer of a substance by convection-diffusion in a laminar fluid.

* In Applications of Advanced Computational Methods for Boundary and Interior Layers;*

#### Peer Reviewed Journals

Parameter-uniform numerical method for singularly perturbed convection-diffusion problem on a circular domain

Hegarty, AF,O'Riordan, E

(2017)
Parameter-uniform numerical method for singularly perturbed convection-diffusion problem on a circular domain

* In Advances In Computational Mathematics;*
pp. 885-909

**DOI:** 10.1007/s10444-016-9510-z

A shunted model of renal inner medulla with pre-bend transitions: Comparison with multi-nephron models.

Gonzalez M, Thomas SR, Hegarty AF

(2009)
A shunted model of renal inner medulla with pre-bend transitions: Comparison with multi-nephron models.

* In Faseb Journal;*
pp. 818.7-818.7-818.7-818.7

**DOI:** 10.1096/fj.1530-6860

Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient

Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI

(2004)
Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient

* In Mathematical And Computer Modelling;*
pp. 1375-1392

**DOI:** 10.1016/j.mcm.2005.01.025

Singularly perturbed convection-diffusion problems with boundary and weak interior layers

Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI

(2004)
Singularly perturbed convection-diffusion problems with boundary and weak interior layers

* In Journal Of Computational And Applied Mathematics;*
pp. 133-151

**DOI:** 10.1016/j.cam.2003.09.033

Numerical solution of a convection diffusion problem with Robin boundary conditions

Ansari, AR; Hegarty, AF

(2003)
Numerical solution of a convection diffusion problem with Robin boundary conditions

* In Journal Of Computational And Applied Mathematics;*
pp. 221-238

**DOI:** 10.1016/S0377-0427(02)00913-5

A note on fitted operator methods for a laminar jet problem

Ansari, AR; Hegarty, AF; Shishkin, GI

(2003)
A note on fitted operator methods for a laminar jet problem

* In Applied Numerical Mathematics;*
pp. 353-365

**DOI:** 10.1016/S0168-9274(02)00225-8

A note on iterative methods for solving singularly perturbed problems using non-monotone methods on Shishkin meshes

Ansari, AR; Hegarty, AF

(2003)
A note on iterative methods for solving singularly perturbed problems using non-monotone methods on Shishkin meshes

* In Computer Methods In Applied Mechanics And Engineering;*
pp. 3673-3687

**DOI:** 10.1016/S0045-7825(03)00369-4

Parameter-uniform numerical methods for a laminar jet problem

Ansari, AR; Hegarty, AF; Shishkin, GI

(2003)
Parameter-uniform numerical methods for a laminar jet problem

* In International Journal For Numerical Methods In Fluids;*
pp. 937-951

**DOI:** 10.1002/fld.511

Numerical solution of a rimming flow problem using a moving mesh method.

Hegarty, AF;O'Brien, SB; Sikwila, S

(2003)
Numerical solution of a rimming flow problem using a moving mesh method.

* In Computational Methods In Applied Mathematics;*
pp. 373-386

Numerical techniques for flow problems with singularities

Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI

(2003)
Numerical techniques for flow problems with singularities

* In International Journal For Numerical Methods In Fluids;*
pp. 915-936

**DOI:** 10.1002/fld.536

Computing realistic Reynolds-uniform error bound's for discrete derivatives of flow velocities in the boundary layer for Prandtl's problem

Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI

(2003)
Computing realistic Reynolds-uniform error bound's for discrete derivatives of flow velocities in the boundary layer for Prandtl's problem

* In International Journal For Numerical Methods In Fluids;*
pp. 895-902

**DOI:** 10.1002/fld.573

An experimental technique for computing parameter-uniform error estimates for numerical solutions of singular perturbation problems, with an application to Prandtl's problem at high Reynolds number

Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI

(2002)
An experimental technique for computing parameter-uniform error estimates for numerical solutions of singular perturbation problems, with an application to Prandtl's problem at high Reynolds number

* In Applied Numerical Mathematics;*
pp. 143-149

**DOI:** 10.1016/S0168-9274(01)00073-3

On a necessary requirement for re-uniform numerical methods to solve boundary layer equations for flow along a flat plate

Shishkin, GI; Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E

(2001)
On a necessary requirement for re-uniform numerical methods to solve boundary layer equations for flow along a flat plate

* In Numerical Analysis And Its Applications;*
Err:511(Ed.)
pp. 723-731

On a necessary requirement for re-uniform numerical methods to solve boundary layer equations for flow along a flat plate

Shishkin, GI; Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E

(2001)
On a necessary requirement for re-uniform numerical methods to solve boundary layer equations for flow along a flat plate

* In Lecture Notes In Computer Science;*
pp. 723-731

Parameter-uniform numerical methods for a class of singularly perturbed problems with a Neumann boundary condition

Farrell, PA; Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI

(2001)
Parameter-uniform numerical methods for a class of singularly perturbed problems with a Neumann boundary condition

* In Numerical Analysis And Its Applications;*
Err:511(Ed.)
pp. 292-303

A parameter robust method for a problem with a symmetry boundary layer

Ansari, AR; Hegarty, AF; Shishkin, GI

(2001)
A parameter robust method for a problem with a symmetry boundary layer

* In Numerical Analysis And Its Applications;*
Err:511(Ed.)
pp. 18-26

Numerical results for advection-convection problems on fitted meshes

Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI

(1997)
Numerical results for advection-convection problems on fitted meshes

* In Cwi Quarterly;*
pp. 235-289

ON A NOVEL MESH FOR THE REGULAR BOUNDARY-LAYERS ARISING IN ADVECTION-DOMINATED TRANSPORT IN 2 DIMENSIONS

HEGARTY, AF; MILLER, JJH; ORIORDAN, E; SHISHKIN, GI

(1995)
ON A NOVEL MESH FOR THE REGULAR BOUNDARY-LAYERS ARISING IN ADVECTION-DOMINATED TRANSPORT IN 2 DIMENSIONS

* In Communications In Numerical Methods In Engineering;*
pp. 435-441

**DOI:** 10.1002/cnm.1640110508

SPECIAL MESHES FOR FINITE-DIFFERENCE APPROXIMATIONS TO AN ADVECTION-DIFFUSION EQUATION WITH PARABOLIC LAYERS

HEGARTY, AF; MILLER, JJH; ORIORDAN, E; SHISHKIN, GI

(1995)
SPECIAL MESHES FOR FINITE-DIFFERENCE APPROXIMATIONS TO AN ADVECTION-DIFFUSION EQUATION WITH PARABOLIC LAYERS

* In Journal Of Computational Physics;*
pp. 47-54

**DOI:** 10.1006/jcph.1995.1043

NUMERICAL RESULTS FOR ADVECTION-DOMINATED HEAT-TRANSFER IN A MOVING FLUID WITH A NON-SLIP BOUNDARY-CONDITION

HEGARTY, AF; MILLER, JJH; ORIORDAN, E; SHISHKIN, GI

(1995)
NUMERICAL RESULTS FOR ADVECTION-DOMINATED HEAT-TRANSFER IN A MOVING FLUID WITH A NON-SLIP BOUNDARY-CONDITION

* In International Journal Of Numerical Methods For Heat & Fluid Flow;*
pp. 131-140

**DOI:** 10.1108/EUM0000000004115

USE OF CENTRAL-DIFFERENCE OPERATORS FOR SOLUTION OF SINGULARLY PERTURBED PROBLEMS

HEGARTY, AF; MILLER, JJH; ORIORDAN, E; SHISHKIN, GI

(1994)
USE OF CENTRAL-DIFFERENCE OPERATORS FOR SOLUTION OF SINGULARLY PERTURBED PROBLEMS

* In Communications In Numerical Methods In Engineering;*
pp. 297-302

**DOI:** 10.1002/cnm.1640100404

Special numerical methods for convection-dominated laminar flows at arbitrary Reynolds number.

Hegarty, AF; Miller, JJH; O'Riordan, E; Shishkin, GI

(1994)
Special numerical methods for convection-dominated laminar flows at arbitrary Reynolds number.

* In J. Numerical Mathematics;*
pp. 65-74

A COMPARISON OF UNIFORMLY CONVERGENT DIFFERENCE-SCHEMES FOR 2-DIMENSIONAL CONVECTION DIFFUSION-PROBLEMS

HEGARTY, AF; ORIORDAN, E; STYNES, M

(1993)
A COMPARISON OF UNIFORMLY CONVERGENT DIFFERENCE-SCHEMES FOR 2-DIMENSIONAL CONVECTION DIFFUSION-PROBLEMS

* In Journal Of Computational Physics;*
pp. 24-32

**DOI:** 10.1006/jcph.1993.1050

#### Conference Publications

6th International Conference on Boundary and Interior Layers (BAIL VI)

Hegarty A.F., Miller J.J.H., O'Riordan E. and Shishkin G.I.,Menakuru, S.,Ahmed, J.,Larvin, M.,Leeder, P.

(2012)
6th International Conference on Boundary and Interior Layers (BAIL VI)

* In British Journal of Surgery;*
J.J.H. Miller(Ed.)
pp. 67-68

Lecture Notes in Computational Science and Engineering

Hegarty A.F., Gonzalez M., Thomas S.R.

(2009)
Lecture Notes in Computational Science and Engineering

pp. 153-161

**DOI:** 10.1007/978-3-642-00605-0_11

AIP Conference Proceedings

Gonzalez M.T., Hegarty A.F., Thomas S.R.

(2009)
AIP Conference Proceedings

pp. 1469-1471

**DOI:** 10.1063/1.3241372

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS 1 AND 2

Gonzalez, MT; Hegarty, AF; Thomas, SR

(2009)
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS 1 AND 2

pp. 1469-1471

BAIL 2006

Branley, D., Hegarty, A.F., Purtill, H., Shishkin, G.I.

(2006)
BAIL 2006

G. Lube, G. Rapin(Ed.)
pp. *-*

BAIL 2006

Hegarty,A.F., Sikwila, S., Shiskin, G.I.

(2006)
BAIL 2006

G. Lube, G.Rapin(Ed.)
pp. *-*

Biennial Numerical Analysis Conference

Sikwila, S., Hegarty, A.F. and Shishkin, G.I.

(2005)
Biennial Numerical Analysis Conference

*(Ed.)
pp. *-*

2nd International Conference, Computational Methods in Applied Mathematics

Sikwila, S., Hegarty, A.F. and Shishkin, G.I.

(2005)
2nd International Conference, Computational Methods in Applied Mathematics

*(Ed.)
pp. *-*

3rd Annual Workshop on Numerical Methods for Problems with Layer Phenomena

Ansari, A.R., Hegarty, A.F. and Shishkin, G.I.

(2004)
3rd Annual Workshop on Numerical Methods for Problems with Layer Phenomena

Ansari, A.R., Hegarty, A.F. and Shishkin, G.I.(Ed.)
pp. 70-75

BAIL 2004

Sikwila, S., Hegarty, A.F. and Shishkin, G.I.

(2004)
BAIL 2004

*(Ed.)
pp. *-*

BAIL 2004

Ansari, A.R., Hegarty, A.F. and Shishkin, G.I.

(2004)
BAIL 2004

*(Ed.)
pp. *-*

3rd Annual Workshop on Numerical Methods for Problems with Layer Phenomena

Sikwila, S., Hegarty, A.F. and Shishkin, G.I.,

(2004)
3rd Annual Workshop on Numerical Methods for Problems with Layer Phenomena

Ansari, A.R., Hegarty, A.F. and Shishkin, G.I.(Ed.)
pp. 52-58

BAIL 2002

Farrell, P.A., Hegarty, A.F., Miller, J.J.H., O'Riordan, E. and Shishkin. G.I.

(2002)
BAIL 2002

S.Wang(Ed.)
pp. 115-120

BAIL 2002

Ansari, A.R. and Hegarty, A.F.

(2002)
BAIL 2002

*(Ed.)
pp. 43-48

Eccomas Computational Fluid Dynamics Conference

Ansari A.R., Hegarty A.F. and Shishkin G.I.

(2001)
Eccomas Computational Fluid Dynamics Conference

*(Ed.)
pp. *-*

Eccomas Computational Fluid Dynamics Conference

Farrell P.A., Hegarty A.F., Miller J.J.H., O'Riordan E. and Shishkin G.I.

(2001)
Eccomas Computational Fluid Dynamics Conference

*(Ed.)
pp. *-*

International Seminar on Applied Mathematics '91

O'Riordan E., Hegarty A.F. and Stynes M.

(1999)
International Seminar on Applied Mathematics '91

H.-G. Roos, A. Felgenhauer, L. Angermann(Ed.)
pp. 91-96

Meeting on Singular Perturbation Problems

Hegarty A.F.

(1995)
Meeting on Singular Perturbation Problems

*(Ed.)
pp. *-*

September Meeting, Irish Mathematical Society

Hegarty, A.F.

(1995)
September Meeting, Irish Mathematical Society

*(Ed.)
pp. *-*

BAIL VI

HEGARTY, AF; MILLER, JJH; ORIORDAN, E; SHISHKIN, GI

(1992)
BAIL VI

pp. 67-68

13th IMACS World Congress

Hegarty A.F., Miller J.J.H., O'Riordan E. and Shishkin G.I.

(1991)
13th IMACS World Congress

R. Vichnevetsky and J.J.H. Miller(Ed.)
pp. 503-504

13th IMACS World Congress

Farrell P.A. and Hegarty A.F.

(1991)
13th IMACS World Congress

R. Vichnevetsky and J.J.H. Miller(Ed.)
pp. 501-502

Fourth International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL IV)

Hegarty, A.F.

(1986)
Fourth International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL IV)

J.J.H. Miller and Novikov(Ed.)
pp. 314-319

Second International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL II)

Hegarty, A.F.

(1982)
Second International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL II)

J.J.H. Miller(Ed.)
pp. 263-268

First International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL I)

Hegarty A.F., Miller J.J.H. and O'Riordan E.

(1980)
First International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL I)

J.J.H. Miller(Ed.)
pp. 301-305

First International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL I)

Farrell P.A., Hegarty A.F., Miller J.J.H., O'Reilly M.J. and Sloane A.A.

(1980)
First International Conference on Computational and Asymptotic Methods for Boundary and Interior Layers (BAIL I)

J.J.H. Miller(Ed.)
pp. 275-280