Error estimates in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems

Publication date: 18 April 2016

Abstract: Error estimates of finite element methods for reaction-diffusion Problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the

H^{1}

seminorm leads to a balanced norm which reflects the layer behavior correctly. We discuss also anisotropic problems, semilinear equations, supercloseness and a combination technique.

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