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Contractivity and Analyticity in l p of Some Approximation of the Heat Equation

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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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  1. Institut de Recherche Mathématique de Rennes, Université de Rennes 1, Campus de Beaulieu, Rennes, France

    Michel Crouzeix

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  1. Michel Crouzeix
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Crouzeix, M. Contractivity and Analyticity in l p of Some Approximation of the Heat Equation. Numerical Algorithms 33, 193–201 (2003). https://doi.org/10.1023/A:1025512021335

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