Boundary corrections on multi-dimensional PDEs
Two new boundary correction techniques are proposed in order to mitigate the order reduction phenomenon associated to the numerical solution of initial boundary value problems for parabolic Partial Differential Equations in arbitrary spatial dimensions with time dependent Dirichlet boundary conditio...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad de La Laguna (ULL) |
| Repositorio: | RIULL. Repositorio Institucional de la Universidad de La Laguna |
| OAI Identifier: | oai:riull.ull.es:915/39061 |
| Acceso en línea: | http://riull.ull.es/xmlui/handle/915/39061 |
| Access Level: | acceso abierto |
| Palabra clave: | High-dimensional PDEs Approximate matrix factorization W-methods Finite differences Order reduction Boundary correction technique |
| Sumario: | Two new boundary correction techniques are proposed in order to mitigate the order reduction phenomenon associated to the numerical solution of initial boundary value problems for parabolic Partial Differential Equations in arbitrary spatial dimensions with time dependent Dirichlet boundary conditions. The new techniques are based on the idea of discretizing the PDE problem at the boundary points as similar as possible to that of the interior points of the domain. These new techniques are considered for the time integration with W-methods based on Approximate Matrix Factorization. By suitably modifying the internal stages of the methods on the boundary points, it is illustrated by numerical testing with time dependent boundary conditions that the new boundary correction techniques are able to keep the same accuracy and order of convergence that the method reaches in the case of homogeneous boundary conditions. |
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