Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square |
| |
Authors: | Castro, Carlos Micu, Sorin Munch, Arnaud |
| |
Affiliation: | Departmento de Matemática e Informática Aplicadas a la Ingeniería Civil, Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, 28040 Madrid, Spain |
| |
Abstract: | Sorin Micu This paper studies the numerical approximation of the boundarycontrol for the wave equation in a square domain. It is knownthat the discrete and semi-discrete models obtained by discretizingthe wave equation with the usual finite-difference or finite-elementmethods do not provide convergent sequences of approximationsto the boundary control of the continuous wave equation as themesh size goes to zero. Here, we introduce and analyse a newsemi-discrete model based on the space discretization of thewave equation using a mixed finite-element method with two differentbasis functions for the position and velocity. The main theoreticalresult is a uniform observability inequality which allows usto construct a sequence of approximations converging to theminimal L2-norm control of the continuous wave equation. Wealso introduce a fully discrete system, obtained from our semi-discretescheme, for which we conjecture that it provides a convergentsequence of discrete approximations as both h and t, the timediscretization parameter, go to zero. We illustrate this factwith several numerical experiments. |
| |
Keywords: | exact controllability observability numerical approximation of controls wave equation |
本文献已被 Oxford 等数据库收录! |
|