Summary.
We consider an interior penalty discontinuous approximation for symmetric elliptic problems of second order on non-matching grids in this paper. The main result is an almost optimal error estimate for the interior penalty approximation of the original problem based on partitioning of the domain into a finite number of subdomains. Further, an error analysis for the finite element approximation of the penalty formulation is given. Finally, numerical experiments on a series of model second order problems are presented.
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Mathematics Subject Classification (2000): 65F10, 65N20, 65N30
The work of the first and the second authors has been partially supported by the National Science Foundation under Grant DMS-9973328. The work of the last author was performed under the auspices of the U. S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract W-7405-Eng-48.
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Lazarov, R., Pasciak, J., Schöberl, J. et al. Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on non-matching grids. Numer. Math. 96, 295–315 (2003). https://doi.org/10.1007/s00211-003-0476-7
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DOI: https://doi.org/10.1007/s00211-003-0476-7