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

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

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. N...

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Veröffentlicht in:Journal of scientific computing 2017-10, Vol.73 (1), p.330-365
Hauptverfasser: Guzmán, Johnny, Sánchez, Manuel A., Sarkis, Marcus
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Estimates
Finite element analysis
Finite element method
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Neighborhoods
Numerical analysis
Theoretical
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Zusammenfassung: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-017-0415-x