Comparison of the High-Order Compact Difference and Discontinuous Galerkin Methods in Computations of the Incompressible Flow

2011 ◽  
pp. 191-196 ◽  
Author(s):  
Artur Tyliszczak ◽  
Maciej Marek ◽  
Andrzej Boguslawski
Keyword(s):  
Discontinuous Galerkin ◽  
Incompressible Flow ◽  
Discontinuous Galerkin Methods ◽  
High Order ◽  
Galerkin Methods ◽  
Compact Difference

Stabilized hp-DGFEM for Incompressible Flow

2003 ◽  
Vol 13 (10) ◽  
pp. 1413-1436 ◽  
Author(s):  
D. Schötzau ◽  
C. Schwab ◽  
A. Toselli
Keyword(s):  
Boundary Layer ◽  
Discontinuous Galerkin ◽  
Incompressible Flow ◽  
Discontinuous Galerkin Methods ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Stability Result ◽  
Approximation Order ◽  
Galerkin Methods ◽  
Aspect Ratios

We consider stabilized mixed hp-discontinuous Galerkin methods for the discretization of the Stokes problem in three-dimensional polyhedral domains. The methods are stabilized with a term penalizing the pressure jumps. For this approach it is shown that ℚk-ℚk and ℚk-ℚk-1 elements satisfy a generalized inf–sup condition on geometric edge and boundary layer meshes that are refined anisotropically and non quasi-uniformly towards faces, edges, and corners. The discrete inf–sup constant is proven to be independent of the aspect ratios of the anisotropic elements and to decrease as k-1/2 with the approximation order. We also show that the generalized inf–sup condition leads to a global stability result in a suitable energy norm.

High-Order Mesh Generation for Discontinuous Galerkin Methods Based on Elastic Deformation

2016 ◽  
Vol 8 (4) ◽  
pp. 693-702
Author(s):  
Hongqiang Lu ◽  
Kai Cao ◽  
Lechao Bian ◽  
Yizhao Wu
Keyword(s):  
Finite Element Method ◽  
Discontinuous Galerkin ◽  
Mesh Generation ◽  
Discontinuous Galerkin Methods ◽  
Elasticity Modulus ◽  
High Order ◽  
Galerkin Methods ◽  
Governing Equations ◽  
Numerical Tests ◽  
Cubic Polynomial

AbstractIn this paper, a high-order curved mesh generation method for Discontinuous Galerkin methods is introduced. First, a regular mesh is generated. Second, the solid surface is re-constructed using cubic polynomial. Third, the elastic governing equations are solved using high-order finite element method to provide a fully or partly curved grid. Numerical tests indicate that the intersection between element boundaries can be avoided by carefully defining the elasticity modulus.

High order discontinuous Galerkin methods on simplicial elements for the elastodynamics equation

2015 ◽  
Vol 71 (1) ◽  
pp. 181-206 ◽  
Author(s):  
Paola F. Antonietti ◽  
Carlo Marcati ◽  
Ilario Mazzieri ◽  
Alfio Quarteroni
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
High Order ◽  
Galerkin Methods
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