Boundary integral equations for the heat equation

Víctor Domínguez ^[1] ; Francisco Javier Sayas ^[1]
1. [1] Universidad de Zaragoza
  
  Universidad de Zaragoza
  
  Zaragoza, España
Localización: XVII Congreso de Ecuaciones Diferenciales y Aplicaciones ; VII Congreso de Matemática Aplicada: Salamanca, 14-28 septiembre 2001 / coord. por Luis Ferragut Canals, Anastasio Pedro Santos Yanguas, 2001, ISBN 8469961446, págs. 407-408
Idioma: inglés
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Resumen
- This work deals with the solution of the Dirichlet problem for the heat equation in the exterior of a domain with smooth boundary in the plane using Bound- ary Integral Methods. We prove that in some particular cases the error committed when solving the corresponding integral equations by a particular Galerkin scheme (spectral in space, piecewise constant in time) admits an error expansion in terms of the time discretization parameter. In addition, a pointwise superconvergence resultis proven at particular instants of time. Finally some numerical experiments are shown corroborating the theory.