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

A. F. Hegarty; E. O'Riordan

doi:10.1016/j.cam.2022.114155

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

A. F. Hegarty, E. O'Riordan

Department of Mathematics and Statistics

Dublin City University

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

Abstract

A numerical algorithm is presented to solve a benchmark problem proposed by Hemker (1996). The algorithm incorporates asymptotic information into the design of appropriate piecewise-uniform Shishkin meshes. Moreover, different co-ordinate systems are utilized due to the different geometries and associated layer structures that are involved in this problem. Numerical results are presented to demonstrate the effectiveness of the proposed numerical algorithm.

Original language	English
Article number	114155
Journal	Journal of Computational and Applied Mathematics
Volume	409
DOIs	https://doi.org/10.1016/j.cam.2022.114155
Publication status	Published - 1 Aug 2022

Keywords

Hemker problem
Shishkin mesh
Singularly perturbed

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10.1016/j.cam.2022.114155

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title = "A numerical algorithm to computationally solve the Hemker problem using Shishkin meshes",

abstract = "A numerical algorithm is presented to solve a benchmark problem proposed by Hemker (1996). The algorithm incorporates asymptotic information into the design of appropriate piecewise-uniform Shishkin meshes. Moreover, different co-ordinate systems are utilized due to the different geometries and associated layer structures that are involved in this problem. Numerical results are presented to demonstrate the effectiveness of the proposed numerical algorithm.",

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AU - O'Riordan, E.

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N2 - A numerical algorithm is presented to solve a benchmark problem proposed by Hemker (1996). The algorithm incorporates asymptotic information into the design of appropriate piecewise-uniform Shishkin meshes. Moreover, different co-ordinate systems are utilized due to the different geometries and associated layer structures that are involved in this problem. Numerical results are presented to demonstrate the effectiveness of the proposed numerical algorithm.

AB - A numerical algorithm is presented to solve a benchmark problem proposed by Hemker (1996). The algorithm incorporates asymptotic information into the design of appropriate piecewise-uniform Shishkin meshes. Moreover, different co-ordinate systems are utilized due to the different geometries and associated layer structures that are involved in this problem. Numerical results are presented to demonstrate the effectiveness of the proposed numerical algorithm.

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KW - Shishkin mesh

KW - Singularly perturbed

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

Abstract

Keywords

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