On some time marching schemes for the stabilized finite element approximation of the mixed wave equation
In this paper we analyze time marching schemes for the wave equation in mixed form. The problem is discretized in space using stabilized finite elements. On the one hand, stability and convergence analyses of the fully discrete numerical schemes are presented using different time integration schemes...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/81095 |
| Acceso en línea: | https://hdl.handle.net/2117/81095 https://dx.doi.org/10.1016/j.cma.2015.07.016 |
| Access Level: | acceso abierto |
| Palabra clave: | Wave equation Time marching schemes Dispersion Dissipation von Neumann analysis Fourier analysis Mixed wave equation VARIATIONAL MULTISCALE METHOD ORTHOGONAL SUBSCALES TRANSPORT PROBLEMS LOW-DISSIPATION CONVERGENCE DISPERSION STOKES FORM DISCRETIZATION FORMULATIONS Ones (Matemàtica) Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
| Sumario: | In this paper we analyze time marching schemes for the wave equation in mixed form. The problem is discretized in space using stabilized finite elements. On the one hand, stability and convergence analyses of the fully discrete numerical schemes are presented using different time integration schemes and appropriate functional settings. On the other hand, we use Fourier techniques (also known as von Neumann analysis) in order to analyze stability, dispersion and dissipation. Numerical convergence tests are presented for various time integration schemes, polynomial interpolations (for the spatial discretization), stabilization methods, and variational forms. To analyze the behavior of the different schemes considered, a 1D wave propagation problem is solved. (C) 2015 Elsevier B.V. All rights reserved. |
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