Discontinuous Galerkin Methods Using an hp-Multigrid Solver for Inviscid Compressible Flows on Three-dimensional Unstructured Meshes

2006 ◽  
Author(s):  
Cristian Nastase ◽  
Dimitri Mavriplis
Keyword(s):  
Discontinuous Galerkin ◽  
Compressible Flows ◽  
Discontinuous Galerkin Methods ◽  
Three Dimensional ◽  
Unstructured Meshes ◽  
Galerkin Methods ◽  
Multigrid Solver ◽  
Inviscid Compressible Flows

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.

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