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

Johnny Guzmán; Manuel A. Sánchez; Marcus Sarkis

doi:10.1007/s10915-017-0415-x

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

Johnny Guzmán
, Manuel A. Sánchez
, Marcus Sarkis

Research output: Contribution to journal › Article › peer-review

47 Scopus citations

Abstract

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 L² norm and H¹ weighted semi-norm independent of the contrast between the coefficients. Numerical experiments validating our theoretical findings are provided.

Original language	English (US)
Pages (from-to)	330-365
Number of pages	36
Journal	Journal of Scientific Computing
Volume	73
Issue number	1
DOIs	https://doi.org/10.1007/s10915-017-0415-x
State	Published - Oct 1 2017
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media New York.

Keywords

Finite elements
High-contrast
Interface problems

Publisher link

10.1007/s10915-017-0415-x

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abstract = "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 L2 norm and H1 weighted semi-norm independent of the contrast between the coefficients. Numerical experiments validating our theoretical findings are provided.",

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AB - 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 L2 norm and H1 weighted semi-norm independent of the contrast between the coefficients. Numerical experiments validating our theoretical findings are provided.

KW - Finite elements

KW - High-contrast

KW - Interface problems

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UR - https://www.scopus.com/pages/publications/85015681696#tab=citedBy

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

Abstract

Bibliographical note

Keywords

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