Sharp Expressions for the Stabilization Parameters in Symmetric Interior-penalty Discontinuous Galerkin Finite Element Approximations of Fourth-order Elliptic Problems

2007 ◽  
Vol 7 (4) ◽  
pp. 365-375 ◽  
Author(s):  
I. Mozolevski ◽  
P.R. Bösing
Keyword(s):  
Finite Element ◽  
Discontinuous Galerkin ◽  
Fourth Order ◽  
Elliptic Problems ◽  
Penalty Parameter ◽  
Interior Penalty ◽  
Galerkin Finite Element ◽  
Finite Element Approximations ◽  
Discontinuous Galerkin Finite Element ◽  
Parameter Values

Abstract In this paper, we derive explicit expressions for the penalty parameters appearing in symmetric and semi-symmetric interior-penalty discontinuous Galerkin finite element method (DGFEM) for fourth-order elliptic problems. We demonstrate the sharpness of the theoretically predicted penalty parameter values through numerical experiments.

A NEW INTERIOR PENALTY DISCONTINUOUS GALERKIN METHOD FOR THE REISSNER–MINDLIN MODEL

2010 ◽  
Vol 20 (08) ◽  
pp. 1343-1361 ◽  
Author(s):  
PAULO R. BÖSING ◽  
ALEXANDRE L. MADUREIRA ◽  
IGOR MOZOLEVSKI
Keyword(s):  
Finite Element ◽  
Discontinuous Galerkin ◽  
A Priori ◽  
Mindlin Plate ◽  
Interior Penalty ◽  
Galerkin Finite Element ◽  
Discontinuous Galerkin Finite Element ◽  
Integration Techniques ◽  
Galerkin Finite Element Methods ◽  
Half Thickness

We introduce an interior penalty discontinuous Galerkin finite element method for the Reissner–Mindlin plate model that, as the plate's half-thickness ϵ tends to zero, recovers a hp interior penalty discontinuous Galerkin finite element methods for biharmonic equation. Our method does not introduce shear as an extra unknown, and does not need reduced integration techniques. We develop the a priori error analysis of these methods and prove error bounds that are optimal in h and uniform in ϵ. Numerical tests, that confirm our predictions, are provided.

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