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The Rothe method for the wave equation in several space dimensions

Published online by Cambridge University Press:  14 November 2011

Erich Martensen
Erich Martensen
Affiliation:
Mathematisches Institut II, Universität Karlsruhe
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Synopsis

The interior initial-boundary value problem for the wave equation in m ≧ 1 space dimension is considered for vanishing boundary values. Certain regularity, dependent on m, is required for the solution and additionalboundary conditions, the number of which being also dependent on m, are imposed on the given right hand side. Emphazising the case m = 3, the Rothe method is applied after the problem has been rewritten as a hyperbolic first order evolution problem for m + 1 unknown functions. The sequence of discrete solutions obtained is shown to be discretely convergent to the continuous solution in the sense of uniform convergence if the solution of the continuous problem is assumed to exist. A priori estimates are derived both for the discrete solutions and the continuous solution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 1-2 , 1979 , pp. 1 - 18
Copyright
Copyright © Royal Society of Edinburgh 1979

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