On nonlinear artificial viscosity,discrete maximum principle and hyperbolic conservation laws |
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Authors: | Erik Burman |
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Institution: | (1) Institute of Analysis and Scientific Computing, Ecole Polytechnique Fédérale de Lausanne, Station 8, CH-1015 Lausanne, Switzerland |
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Abstract: | A finite element method for Burgers’ equation is studied. The method is analyzed using techniques from stabilized finite element
methods and convergence to entropy solutions is proven under certain hypotheses on the artificial viscosity. In particular
we assume that a discrete maximum principle holds. We then construct a nonlinear artificial viscosity that satisfies the assumptions
required for convergence and that can be tuned to minimize artificial viscosity away from local extrema.
The theoretical results are exemplified on a numerical example.
AMS subject classification (2000) 65M20, 65M12, 35L65, 76M10 |
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Keywords: | conservation laws monotone scheme discrete maximum principle stabilized finite element methods artificial viscosity slope limiter |
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