A balancing domain decomposition by constraints preconditioner for a weakly over-penalized symmetric interior penalty method

2012 ◽  
Vol 20 (3) ◽  
pp. 472-491 ◽  
Author(s):  
Susanne C. Brenner ◽  
Eun-Hee Park ◽  
Li-Yeng Sung
Keyword(s):  
Domain Decomposition ◽  
Penalty Method ◽  
Interior Penalty ◽  
Balancing Domain Decomposition ◽  
Interior Penalty Method ◽  
Symmetric Interior Penalty Method

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.

A Posteriori Error Estimates of a Weakly Over-Penalized Symmetric Interior Penalty Method for Elliptic Eigenvalue Problems

2015 ◽  
Vol 5 (4) ◽  
pp. 327-341
Author(s):  
Yuping Zeng ◽  
Jinru Chen ◽  
Feng Wang
Keyword(s):  
Penalty Method ◽  
Eigenvalue Problems ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Error Estimator ◽  
Interior Penalty ◽  
Numerical Tests ◽  
Interior Penalty Method ◽  
Symmetric Interior Penalty Method ◽  
Elliptic Eigenvalue Problems

AbstractA weakly over-penalized symmetric interior penalty method is applied to solve elliptic eigenvalue problems. We derive a posteriori error estimator of residual type, which proves to be both reliable and efficient in the energy norm. Some numerical tests are provided to confirm our theoretical analysis.

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