Quasi-optimal nonconforming approximation of elliptic PDES with contrasted coefficients and minimal regularity

Abstract : In this paper we investigate the approximation of a diffusion model problem with contrasted diffusivity and the error analysis of various nonconforming approximation methods. The essential difficulty is that the Sobolev smoothness index of the exact solution may be just barely larger than one. The lack of smoothness is handled by giving a weak meaning to the normal derivative of the exact solution at the mesh faces. The error estimates are robust with respect to the diffusivity contrast. We briefly show how the analysis can be extended to the Maxwell's equations.
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Contributor : Alexandre Ern <>
Submitted on : Friday, December 21, 2018 - 8:15:17 PM
Last modification on : Friday, April 19, 2019 - 4:55:02 PM
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Alexandre Ern, Jean-Luc Guermond. Quasi-optimal nonconforming approximation of elliptic PDES with contrasted coefficients and minimal regularity. 2018. ⟨hal-01964299⟩

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