A priori analysis for the semi-discrete approximation to the nonlinear damped wave equation
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 $L_{2}(\Omega)$...
| Main Authors: | , |
|---|---|
| Format: | Report |
| Published: |
Unspecified
2000
|
| _version_ | 1797066120397586432 |
|---|---|
| author | Suli, E Wilkins, C |
| author_facet | Suli, E Wilkins, C |
| author_sort | Suli, E |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T21:37:50Z |
| format | Report |
| id | oxford-uuid:46dfd294-f080-4f06-902f-c83887277341 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:37:50Z |
| publishDate | 2000 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:46dfd294-f080-4f06-902f-c838872773412022-03-26T15:16:28ZA priori analysis for the semi-discrete approximation to the nonlinear damped wave equationReporthttp://purl.org/coar/resource_type/c_93fcuuid:46dfd294-f080-4f06-902f-c83887277341Mathematical Institute - ePrintsUnspecified2000Suli, EWilkins, CWe 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. |
| spellingShingle | Suli, E Wilkins, C A priori analysis for the semi-discrete approximation to the nonlinear damped wave equation |
| title | A priori analysis for the semi-discrete approximation to the nonlinear damped wave equation |
| title_full | A priori analysis for the semi-discrete approximation to the nonlinear damped wave equation |
| title_fullStr | A priori analysis for the semi-discrete approximation to the nonlinear damped wave equation |
| title_full_unstemmed | A priori analysis for the semi-discrete approximation to the nonlinear damped wave equation |
| title_short | A priori analysis for the semi-discrete approximation to the nonlinear damped wave equation |
| title_sort | priori analysis for the semi discrete approximation to the nonlinear damped wave equation |
| work_keys_str_mv | AT sulie apriorianalysisforthesemidiscreteapproximationtothenonlineardampedwaveequation AT wilkinsc apriorianalysisforthesemidiscreteapproximationtothenonlineardampedwaveequation AT sulie priorianalysisforthesemidiscreteapproximationtothenonlineardampedwaveequation AT wilkinsc priorianalysisforthesemidiscreteapproximationtothenonlineardampedwaveequation |