Alan Hegarty

2024

A higher order numerical method for singularly perturbed elliptic problems with characteristic boundary layers

Hegarty, A. F. & O'Riordan, E., Jul 2024, In: Applied Numerical Mathematics. 201, p. 85-101 17 p.

Research output: Contribution to journal › Article › peer-review

Open Access

Fitted finite element methods for singularly perturbed elliptic problems of convection-diffusion type

Hegarty, A. F. & O'Riordan, E., Feb 2024, In: Applied Numerical Mathematics. 196, p. 183-198 16 p.

Research output: Contribution to journal › Article › peer-review

Open Access

2022

A numerical algorithm to computationally solve the Hemker problem using Shishkin meshes

Hegarty, A. F. & O'Riordan, E., 1 Aug 2022, In: Journal of Computational and Applied Mathematics. 409, 114155.

Research output: Contribution to journal › Article › peer-review

Open Access

A Numerical Method for Singularly Perturbed Convection-diffusion Problems Posed on Smooth Domains

Hegarty, A. F. & O’Riordan, E., Sep 2022, In: Journal of Scientific Computing. 92, 3, 84.

Research output: Contribution to journal › Article › peer-review

Open Access

2020

A numerical method for the hemker problem

Hegarty, A. F. & O’Riordan, E., 2020, Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2018. Barrenechea, G. R. & Mackenzie, J. (eds.). Springer, p. 97-111 15 p. (Lecture Notes in Computational Science and Engineering; vol. 135).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2019

A parameter-uniform numerical method for a singularly perturbed convection–diffusion problem posed on an annulus

Hegarty, A. F. & O'Riordan, E., 15 Nov 2019, In: Computers and Mathematics with Applications. 78, 10, p. 3329-3344 16 p.

Research output: Contribution to journal › Article › peer-review

Open Access

2017

Numerical Results for Singularly Perturbed Convection-Diffusion Problems on an Annulus

Hegarty, A. F. & O’Riordan, E., 2017, Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2016. Stynes, M., Zhang, Z. & Huang, Z. (eds.). Springer Verlag, p. 101-112 12 p. (Lecture Notes in Computational Science and Engineering; vol. 120).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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

Hegarty, A. F. & O’Riordan, E., 1 Oct 2017, In: Advances in Computational Mathematics. 43, 5, p. 885-909 25 p.

Research output: Contribution to journal › Article › peer-review

2012

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

Hegarty, A., 2012.

Research output: Contribution to conference › Paper

2009

AIP Conference Proceedings

Fowler, A., Fowler, A., Mitchell, S., Vynnycky, M. & Hegarty, A., 2009.

Research output: Contribution to conference › Paper

Open Access

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

Hegarty, A., 2009, In: FASEB Journal. p. 818.7-818.7-818.7-818.7

Research output: Contribution to journal › Article › peer-review

Open Access

A shunt model of the inner medullary nephron with pre-bend transitions

Gonzalez, M. T., Hegarty, A. F. & Thomas, S. R., 2009, Numerical Analysis and Applied Mathematics - International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009. p. 1469-1471 3 p. (AIP Conference Proceedings; vol. 1168).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Glycolysis as a source of "External Osmoles": The vasa recta transient model

Hegarty, A. F., Gonzalez, M. & Thomas, S. R., 2009, BAIL 2008 - Boundary and Interior Layers - Proceedings of the International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods. p. 153-161 9 p. (Lecture Notes in Computational Science and Engineering; vol. 69 LNCSE).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Lecture Notes in Computational Science and Engineering: Preface

Hegarty, A. F., Kopteva, N., O'Riordan, E. & Stynes, M., 2009, In: Lecture Notes in Computational Science and Engineering. 69 LNCSE, p. V

Research output: Contribution to journal › Editorial

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS 1 AND 2

Fowler, A., Mitchell, S., Vynnycky, M. & Hegarty, A., 2009.

Research output: Contribution to conference › Paper

2006

BAIL 2006

Hegarty, A. & Purtill, H., 2006.

Research output: Contribution to conference › Paper

2005

2nd International Conference, Computational Methods in Applied Mathematics

Hegarty, A., 2005.

Research output: Contribution to conference › Paper

Biennial Numerical Analysis Conference

Hegarty, A., 2005.

Research output: Contribution to conference › Paper

2004

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

Hegarty, A., 2004.

Research output: Contribution to conference › Paper

BAIL 2004

Hegarty, A., 2004.

Research output: Contribution to conference › Paper

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

Farrell, P. A., Hegarty, A. F., Miller, J. J. H., O'Riordan, E. & Shishkin, G. I., Dec 2004, In: Mathematical and Computer Modelling. 40, 11-12, p. 1375-1392 18 p.

Research output: Contribution to journal › Article › peer-review

Open Access

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

Farrell, P. A., Hegarty, A. F., Miller, J. J. H., O'Riordan, E. & Shishkin, G. I., 1 Apr 2004, In: Journal of Computational and Applied Mathematics. 166, 1, p. 133-151 19 p.

Research output: Contribution to journal › Article › peer-review

Open Access

2003

A note on fitted operator methods for a laminar jet problem

Ansari, A. R., Hegarty, A. F. & Shishkin, G. I., Jun 2003, In: Applied Numerical Mathematics. 45, 4, p. 353-365 13 p.

Research output: Contribution to journal › Article › peer-review

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

Ansari, A. R. & Hegarty, A. F., 15 Aug 2003, In: Computer Methods in Applied Mechanics and Engineering. 192, 33-34, p. 3673-3687 15 p.

Research output: Contribution to journal › Article › peer-review

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

Farrell, P. A., Hegarty, A. F., Miller, J. J. H., O'Riordan, E. & Shishkin, G. I., 20 Nov 2003, In: International Journal for Numerical Methods in Fluids. 43, 8, p. 895-902 8 p.

Research output: Contribution to journal › Article › peer-review

Open Access

Numerical solution of a convection diffusion problem with Robin boundary conditions

Ansari, A. R. & Hegarty, A. F., 1 Jul 2003, In: Journal of Computational and Applied Mathematics. 156, 1, p. 221-238 18 p.

Research output: Contribution to journal › Article › peer-review

Open Access

Numerical Solution of a Rimming Flow Problem Using a Moving Mesh Method

Hegarty, A. F., O'Brien, S. B. G. & Sikwila, S., 2003, In: Computational Methods in Applied Mathematics. 3, 3, p. 373-386 14 p.

Research output: Contribution to journal › Article › peer-review

Open Access

Numerical techniques for flow problems with singularities

Farrell, P. A., Hegarty, A. F., Miller, J. J. H., O'Riordan, E. & Shishkin, G. I., 20 Nov 2003, In: International Journal for Numerical Methods in Fluids. 43, 8, p. 915-936 22 p.

Research output: Contribution to journal › Article › peer-review

Parameter-uniform numerical methods for a laminar jet problem

Ansari, A. R., Hegarty, A. F. & Shishkin, G. I., 20 Nov 2003, In: International Journal for Numerical Methods in Fluids. 43, 8, p. 937-951 15 p.

Research output: Contribution to journal › Article › peer-review

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

Farrell, P. A., Hegarty, A. F., Miller, J. J. H., O'Riordan, E. & Shishkin, G. I., Jan 2002, In: Applied Numerical Mathematics. 40, 1-2, p. 143-149 7 p.

Research output: Contribution to journal › Article › peer-review

BAIL 2002

Hegarty, A., 2002.

Research output: Contribution to conference › Paper

2001

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

Ansari, A. R., Hegarty, A. F. & Shishkin, G. I., 2001, Numerical Analysis and Its Applications - 2nd International Conference, NAA 2000, Revised Papers. Vulkov, L., Yalamov, P. & Waniewski, J. (eds.). Springer Verlag, p. 18-26 9 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 1988).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Eccomas Computational Fluid Dynamics Conference

Hegarty, A., 2001.

Research output: Contribution to conference › Paper

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

Shishkin, G. I., Farrell, P. A., Hegarty, A. F., Miller, J. J. H. & O’Riordan, E., 2001, Numerical Analysis and Its Applications - 2nd International Conference, NAA 2000, Revised Papers. Vulkov, L., Yalamov, P. & Waniewski, J. (eds.). Springer Verlag, p. 723-731 9 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 1988).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Open Access

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

Farrell, P. A., Hegarty, A. F., Miller, J. J., O’Riordan, E. & Shishkin, G. I., 2001, Numerical Analysis and Its Applications - 2nd International Conference, NAA 2000, Revised Papers. Vulkov, L., Yalamov, P. & Waniewski, J. (eds.). Springer Verlag, p. 292-303 12 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 1988).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review