Guido Kanschat's Discontinuous Galerkin Methods for Viscous Incompressible PDF

By Guido Kanschat

ISBN-10: 3835040014

ISBN-13: 9783835040014

ISBN-10: 3835055194

ISBN-13: 9783835055193

Guido Kanschat studies a number of discontinuous Galerkin schemes for elliptic and viscous movement difficulties. commencing from Nitsche's approach for susceptible boundary stipulations, he experiences the inner penalty and LDG equipment. mixed with a good advection discretization, they yield good DG equipment for linear move difficulties of Stokes and Oseen variety that are utilized to the Navier-Stokes challenge. the writer not just offers the analytical ideas used to review those tools but in addition devotes an immense dialogue to the effective numerical resolution of discrete problems.

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Extra info for Discontinuous Galerkin Methods for Viscous Incompressible Flow

Example text

2          = ; 2 & #  # 2  ; 2 = & #  # 2       #  ! 13 (and ?  6) yields     & #  #    #  5 + CHAPTER 2. 7 Remark: Obviously, the analysis above extends to the situation where Dirichlet boundary conditions are imposed on an open subset / & =1 only. g. [Arn82]) in the stabilization parameter on the boundary. The analysis below shows, that the stabilization in our version is indeed more equilibrated (see also [HL02]).

3) where D   1 with D0  D 9  almost everywhere in 1. / and / are the Dirichlet  " /  . and Neumann parts of /  =1, respectively. We have / ! 3). [GT98]). 5) + + CHAPTER 2. 6) We will refer to this last estimate as elliptic regularity. 1 In [Nit71], Nitsche proposed a fully conforming method of treating Dirichlet boundary values in weak form .  9  is a function constant on each edge     achieving stability of the form as well as penalizing violation of
the boundary condition #  # .

23) Typically, we consider a ball of radius K around - or a patch of mesh cells containing -. 3. LOCAL ERROR ESTIMATES 45 We remark, that the function being constant 6 %: inside %: DQG ]HUR RWKHUZLVH IXO¿OOV WKHVH conditions. Still, the function J%: is not required to be constant on the set %: .  will be allowed. 25) ZKLFK DSSUR[LPDWHV WKH SRLQW HYDOXDWLRQ #- if # LV VXI¿FLHQWO\ UHJXODU DQG K  . 26) the regularized distance function with respect to a point -. With %% , we denote a mesh cell containing - and %    )XUWKHUPRUH ZH GH¿QH N as the  -projection of N into the space , of cell-wise constant functions and denote by N, its value on the cell % .

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Discontinuous Galerkin Methods for Viscous Incompressible Flow by Guido Kanschat

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