Spectral discretization of the time‐dependent Stokes problem with mixed boundary conditions

2021 ◽  
Author(s):  
Chaima Bousbiat ◽  
Yasmina Daikh ◽  
Sarra Maarouf
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Stokes Problem ◽  
Mixed Boundary Conditions ◽  
Time Dependent ◽  
Spectral Discretization

scholarly journals Error analysis of an augmented mixed method for the Navier–Stokes problem with mixed boundary conditions

2017 ◽  
Vol 38 (3) ◽  
pp. 1452-1484 ◽  
Author(s):  
Jessika Camaño ◽  
Ricardo Oyarzúa ◽  
Ricardo Ruiz-Baier ◽  
Giordano Tierra
Keyword(s):  
Error Analysis ◽  
Boundary Conditions ◽  
Mixed Method ◽  
Mixed Boundary ◽  
Stokes Problem ◽  
Mixed Boundary Conditions ◽  
Navier Stokes

scholarly journals Finite element convergence for the time-dependent Joule heating problem with mixed boundary conditions

2020 ◽  
Author(s):  
Max Jensen ◽  
Axel Målqvist ◽  
Anna Persson
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Joule Heating ◽  
Adaptive Mesh Refinement ◽  
Mixed Boundary ◽  
Adaptive Mesh ◽  
Mixed Boundary Conditions ◽  
Time Dependent ◽  
Discrete Maximum Principle ◽  
Backward Euler

Abstract We prove strong convergence for a large class of finite element methods for the time-dependent Joule heating problem in three spatial dimensions with mixed boundary conditions on Lipschitz domains. We consider conforming subspaces for the spatial discretization and the backward Euler scheme for the temporal discretization. Furthermore, we prove uniqueness and higher regularity of the solution on creased domains and additional regularity in the interior of the domain. Due to a variational formulation with a cut-off functional, the convergence analysis does not require a discrete maximum principle, permitting approximation spaces suitable for adaptive mesh refinement, responding to the difference in regularity within the domain.

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