Contractivity and Analyticity in l
p
of Some Approximation of the Heat Equation |
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Authors: | Michel Crouzeix |
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Institution: | (1) Institut de Recherche Mathématique de Rennes, Université de Rennes 1, Campus de Beaulieu, Rennes, France |
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Abstract: | We consider the lumped mass method with piecewise linear finite elements in two dimensions. When the triangulation is of Delaunay type it is known that the discrete scheme satisfies a maximum principle. In this work we pursue the analysis and prove that the discrete semi-group is l
p
contractive in a sector, which implies smoothing effects and provide some resolvent estimates. |
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Keywords: | contractivity resolvent estimates finite elements finite differences |
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