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Error estimates for a mixed finite volume method for the p-Laplacian problem

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Abstract

In this work we propose and analyze a mixed finite volume method for the p-Laplacian problem which is based on the lowest order Raviart–Thomas element for the vector variable and the P1 nonconforming element for the scalar variable. It is shown that this method can be reduced to a P1 nonconforming finite element method for the scalar variable only. One can then recover the vector approximation from the computed scalar approximation in a virtually cost-free manner. Optimal a priori error estimates are proved for both approximations by the quasi-norm techniques. We also derive an implicit error estimator of Bank–Weiser type which is based on the local Neumann problems.

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Authors and Affiliations

  1. Department of Mathematics, Korea Advanced Institute of Science and Technology, 373-1 Kusong-Dong, Yusong-gu, Daejeon, 305-701, South Korea

    Kwang Y. Kim

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  1. Kwang Y. Kim
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Correspondence to Kwang Y. Kim.

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This work was supported by the Post-doctoral Fellowship Program of Korea Science & Engineering Foundation (KOSEF).

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Kim, K. Error estimates for a mixed finite volume method for the p-Laplacian problem. Numer. Math. 101, 121–142 (2005). https://doi.org/10.1007/s00211-005-0610-9

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  • DOI: https://doi.org/10.1007/s00211-005-0610-9

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