Article ID Journal Published Year Pages File Type
6892203 Computers & Mathematics with Applications 2018 15 Pages PDF
Abstract
In this paper, we consider a singularly perturbed convection-diffusion equation posed on the unit square, where the solution has two characteristic layers and an exponential layer. A Galerkin finite element method on a Shishkin mesh is used to solve this problem. Its bilinear forms in different subdomains are carefully analyzed by means of a series of integral inequalities; a delicate analysis for the characteristic layers is needed. Based on these estimations, we prove supercloseness bounds of order 3∕2 (up to a logarithmic factor) on triangular meshes and of order 2 (up to a logarithmic factor) on hybrid meshes respectively. The result implies that the hybrid mesh, which replaces the triangles of the Shishkin mesh by rectangles in the exponential layer region, is superior to the Shishkin triangular mesh. Numerical experiments illustrate these theoretical results.
Related Topics
Physical Sciences and Engineering Computer Science Computer Science (General)
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