Finite Element Methods for Interface Problems: Robust and Local Optimal A Priori Error Estimates

Zhiqiang Cai; Shun Zhang

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arXiv · 1509.08166

Finite Element Methods for Interface Problems: Robust and Local Optimal A Priori Error Estimates

Zhiqiang Cai·Shun Zhang

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Abstract

For elliptic interface problems in two- and three-dimensions, this paper establishes a priori error estimates for Crouzeix-Raviart nonconforming, Raviart-Thomas mixed, and discontinuous Galerkin finite element approximations. These estimates are robust with respect to the diffusion coefficient and optimal with respect to local regularity of the solution. Moreover, we obtain these estimates with no assumption on the distribution of the diffusion coefficient.

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Zhiqiang Cai, Shun Zhang. 2015-10-23. Finite Element Methods for Interface Problems: Robust and Local Optimal A Priori Error Estimates. https://arxiv.org/abs/1509.08166

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