A finite element method for high-contrast interface problems with error\n estimates independent of contrast

2015/07/14 by Johnny Guzmán, Guzman, Johnny, Manuel A. Sánchez +3 · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1507.03873

Abstract

We define a new finite element method for a steady state elliptic problem\nwith discontinuous diffusion coefficients where the meshes are not aligned with\nthe interface. We prove optimal error estimates in the L² norm and H¹\nweighted semi-norm independent of the contrast between the coefficients.\nNumerical experiments validating our theoretical findings are provided.\n

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