Error estimates for a mixed finite volume method for the \(p\)-Laplacian problem (Q2486674)
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| Language | Label | Description | Also known as |
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| English | Error estimates for a mixed finite volume method for the \(p\)-Laplacian problem |
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Error estimates for a mixed finite volume method for the \(p\)-Laplacian problem (English)
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5 August 2005
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This work proposes and analyzes a mixed finite volume method for approximating the solution of a nonlinear \(p\)-Laplacian problem with Dirichlet boundary condition. This method uses the lowest order Raviart-Thomas element for the vector variable and the \(P1\) nonconforming element for the scalar variable. Optimal a priori error estimates are proved for both approximations by using quasi-norm techniques. An implicit error estimator of Bank-Weiser type is also derived. These theoretical results are validated by some numerical examples.
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nonlinear \(p\)-Laplacian problem
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a priori error estimates
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implicit error estimator
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mixed finite volume method
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numerical examples
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