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A Finite Element Method for High-Contrast Interface Problems with Error Estimates Independent of Contrast

2017; Springer Science+Business Media; Volume: 73; Issue: 1 Linguagem: Inglês

10.1007/s10915-017-0415-x

1573-7691

Johnny Guzmán, Manuel A. Sánchez, Marcus Sarkis,

Differential Equations and Numerical Methods

We define a new finite element method for a steady state elliptic problem with discontinuous diffusion coefficients where the meshes are not aligned with the interface. We prove optimal error estimates in the $$L^2$$ norm and $$H^1$$ weighted semi-norm independent of the contrast between the coefficients. Numerical experiments validating our theoretical findings are provided.