Capítulo de Libro
Numerical solution of a Laplace equation with data in L1
Autor/es | Casado Díaz, Juan
Chacón Rebollo, Tomás Gómez Mármol, María Macarena Girault, Vivette Murat, François |
Coordinador/Director | Palacios Latasa, Manuel Pedro
Trujillo, David Torrens Iñigo, Juan José Madaune-Tort, Monique López de Silanes Busto, María Cruz Sanz Sáiz, Gerardo |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2003 |
Fecha de depósito | 2015-12-15 |
Publicado en |
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ISBN/ISSN | 8477337209 |
Resumen | In this work, we address the numerical solution of the Laplace equation with
data in L1 by IP1 finite element schemes. Even if this is a simple problem, its analysis is difficult and requires new tools because finite ... In this work, we address the numerical solution of the Laplace equation with data in L1 by IP1 finite element schemes. Even if this is a simple problem, its analysis is difficult and requires new tools because finite element schemes are based on variational formulations which do not lend themselves to estimates in the L1 norm. The approach for analyzing this problem consists in applying some of the techniques that are used by Murat (cf. [5]) and Boccardo & Gallouet (cf. [2]) in constructing the renormalized solution of the problem. The key ingredient is the assumption that all the angles of the grid are acute; then the matrix of the system is an M matrix. Interestingly, with this sole assumption, we prove that uh tends to u in mesure in Ω. |
Cita | Casado Díaz, J., Chacón Rebollo, T.,...,Murat, F. (2003). Numerical solution of a Laplace equation with data in L1. En M. Madaune-Tort, M.C. López de Silanes Busto, G. Sanz Sáiz, M.P. Palacios Latasa, D. Trujillo, J.J. Torrens Iñigo (Ed.), VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques :Jaca, Spain, September 15-17, 2003 .Universidad de Zaragoza. |
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