Convergence in l2 and l¿ norm of one-stage AMF-W-methods for parabolic problems.
For the numerical solution of parabolic problems with linear diffusion term, linearly implicit time integrators are considered. To reduce the cost on the linear algebra level an alternating direction implicit (ADI) approach is applied (so-called AMF-W-methods). The present work proves optimal bounds...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad de La Laguna (ULL) |
| Repositorio: | RIULL. Repositorio Institucional de la Universidad de La Laguna |
| OAI Identifier: | oai:riull.ull.es:915/39033 |
| Acceso en línea: | http://riull.ull.es/xmlui/handle/915/39033 |
| Access Level: | acceso abierto |
| Palabra clave: | Parabolic PDEs time integration W-methods Approximate Matrix Factorization Alternating Direction Implicit schemes convergence |
| Sumario: | For the numerical solution of parabolic problems with linear diffusion term, linearly implicit time integrators are considered. To reduce the cost on the linear algebra level an alternating direction implicit (ADI) approach is applied (so-called AMF-W-methods). The present work proves optimal bounds of the global error for two classes of 1-stage methods in the Euclidean 2 norm as well as in the maximum norm ∞. The bounds are valid under a very weak step size restriction that covers PDE-convergence, where the time step size is of the same order as the spatial grid size. |
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