The Mathematical Institute, University of Oxford, Eprints Archive

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

Suli, Endre and Wilkins, Catherine (2000) A priori analysis for the semi-discrete approximation to the nonlinear damped wave equation. Technical Report. Unspecified. (Submitted)

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Abstract

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.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1297
Deposited By:Lotti Ekert
Deposited On:04 Jun 2011 09:11
Last Modified:04 Jun 2011 09:11

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