Finite element approximation of the Dirichlet problem using the boundary penalty method

1986 ◽  
Vol 49 (4) ◽  
pp. 343-366 ◽  
Author(s):  
John W. Barrett ◽  
Charles M. Elliott
Keyword(s):  
Finite Element ◽  
Dirichlet Problem ◽  
Penalty Method ◽  
Finite Element Approximation ◽  
Element Approximation

scholarly journals ConstrainedC0Finite Element Methods for Biharmonic Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Rong An ◽  
Xuehai Huang
Keyword(s):  
Finite Element ◽  
Error Estimate ◽  
Penalty Method ◽  
Finite Element Approximation ◽  
Optimal Error Estimates ◽  
Element Approximation ◽  
Interior Penalty ◽  
Biharmonic Problem ◽  
Interior Penalty Method ◽  
Symmetric Interior Penalty Method

This paper presents some constrainedC0finite element approximation methods for the biharmonic problem, which include theC0symmetric interior penalty method, theC0nonsymmetric interior penalty method, and theC0nonsymmetric superpenalty method. In the finite element spaces, theC1continuity across the interelement boundaries is obtained weakly by the constrained condition. For theC0symmetric interior penalty method, the optimal error estimates in the brokenH2norm and in theL2norm are derived. However, for theC0nonsymmetric interior penalty method, the error estimate in the brokenH2norm is optimal and the error estimate in theL2norm is suboptimal because of the lack of adjoint consistency. To obtain the optimalL2error estimate, theC0nonsymmetric superpenalty method is introduced and the optimalL2error estimate is derived.

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