A priori analysis for the semi-discrete approximation to the nonlinear damped wave equation

Report

We study the second-order nonlinear damped wave equation semi-discretised in space using standard Galerkin finite element methods. Denoting the analytical solution and the corresponding finite element solution to the given problem by $u$ and $u_{h}$ respectively, we derive an optimal $L_{2}(\Omega)$ error estimate of the form $\max_{t \in [0,T]} \|u(t)-u_{h}(t)\| \leq C(u)h^{m}$, for $(x,t) \in \bar{\Omega} \times [0,T]$, where $\Omega \subset R^{d}, C$ is a positive constant depending on $u,h$ is the grid parameter, and $m > 1 + d/2$, where $m-1$ is the degree of the piecewise polynomials in the finite element test space.

Authors: Suli, E; Wilkins, C

• Publisher: Unspecified
• Publication date: 2000-01-01