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...

Descripción completa

Detalles Bibliográficos
Autores: Hernández Abreu, Domingo, González Pinto, Severiano, E. Hairer
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
Descripción
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.