Supercloseness of the SDFEM on Shishkin triangular meshes for problems with exponential layers
Jin Zhang, Xiaowei Liu
TL;DR
This paper investigates the supercloseness of the SDFEM on Shishkin triangular meshes for problems with exponential layers, providing theoretical analysis and a postprocessing method to improve accuracy.
Contribution
It offers the first analysis of supercloseness for SDFEM on triangular meshes and introduces a simple postprocessing technique for enhanced solution accuracy.
Findings
The supercloseness property is established for SDFEM on Shishkin triangular meshes.
A postprocessing method improves the solution accuracy.
Numerical experiments confirm the theoretical results.
Abstract
In this paper, we analyze the supercloseness property of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes, which is different from one in the case of rectangular meshes. The analysis depends on integral inequalities for the part related to the diffusion in the bilinear form. Moreover, our result allows the construction of a simple postprocessing that yields a more accurate solution. Finally, numerical experiments support these theoretical results.
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Advanced Numerical Methods in Computational Mathematics · Numerical methods for differential equations