A Splitting Method for Nonlinear Conservation Laws with Source Term and Application to Unilateral Obstacle Problems

• Laurent Lévi ^[1] ; Monique Madaune-Tort ^[1] ; Fabrice Peyroutet ^[1]
  1. [1] Université de Pau & CNRS, Laboratoire de Mathématiques Appliquées, ERS 2055, IPRA, France
• 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. 649-650
• Idioma: inglés
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• Resumen

  • We study the approximation of Dirichlet problems for scalar conservation laws with a source term by a time-splitting technique. The convergence is proved for BV -solutions and then an error estimate of order 1 is given. For only bounded solutions the convergence also holds and an error estimate is obtained as soon as the initial datum of the continuous problem has an intermediate regularity property. This splitting method is applied to a unilateral obstacle problem. The convergence is established and in the case of the Cauchy problem an error estimate of order 1/2 is given.