Fully Computable Error Bounds for Discontinuous Galerkin Finite Element Approximations on Meshes with an Arbitrary Number of Levels of Hanging Nodes

2010 ◽  
Vol 47 (6) ◽  
pp. 4112-4141 ◽  
Author(s):  
Mark Ainsworth ◽  
Richard Rankin
Keyword(s):  
Finite Element ◽  
Discontinuous Galerkin ◽  
Error Bounds ◽  
Arbitrary Number ◽  
Galerkin Finite Element ◽  
Hanging Nodes ◽  
Finite Element Approximations ◽  
Discontinuous Galerkin Finite Element ◽  
Computable Error Bounds

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.

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