scholarly journals A penalty method for the time-dependent Stokes problem with the slip boundary condition and its finite element approximation

2017 ◽  
Vol 62 (4) ◽  
pp. 377-403 ◽  
Author(s):  
Guanyu Zhou ◽  
Takahito Kashiwabara ◽  
Issei Oikawa
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Penalty Method ◽  
Stokes Problem ◽  
Finite Element Approximation ◽  
Slip Boundary Condition ◽  
Time Dependent ◽  
Element Approximation ◽  
Slip Boundary

A mixed finite-element method for elliptic operators with Wentzell boundary condition

2018 ◽  
Vol 40 (1) ◽  
pp. 87-108
Author(s):  
Eberhard Bänsch ◽  
Markus Gahn
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Mixed Finite Element ◽  
A Priori ◽  
Mixed Finite Element Method ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Weak Formulation ◽  
Wentzell Boundary Condition ◽  
Polyhedral Domain

Abstract In this paper we introduce and analyze a mixed finite-element approach for a coupled bulk-surface problem of second order with a Wentzell boundary condition. The problem is formulated on a domain with a curved smooth boundary. We introduce a mixed formulation that is equivalent to the usual weak formulation. Furthermore, optimal a priori error estimates between the exact solution and the finite-element approximation are derived. To this end, the curved domain is approximated by a polyhedral domain introducing an additional geometrical error that has to be bounded. A computational result confirms the theoretical findings.

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