RT info:eu-repo/semantics/article
T1 Boundary corrections on multi-dimensional PDEs
A1 Hernández Abreu, Domingo
A1 González Pinto, Severiano
A1 Pérez Rodríguez, María Soledad
A2 Análisis Matemático
A2 Grupo de investigación ULL:
"Métodos numéricos en ecuaciones diferenciales"
https://www.ull.es/grupoinvestigacion/met-numericos-ec-diferenciales/
K1 High-dimensional PDEs
K1 Approximate matrix factorization
K1 W-methods
K1 Finite differences
K1 Order reduction
K1 Boundary correction technique
AB 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.
YR 2024
FD 2024
LK http://riull.ull.es/xmlui/handle/915/39061
UL http://riull.ull.es/xmlui/handle/915/39061
LA Inglés
DS Repositorio institucional de la Universidad de La Laguna
RD 22-dic-2024