Premium
A note on upwinding and anisotropic balancing dissipation in finite element approximations to convective diffusion problems
Author(s) -
Kelly D. W.,
Nakazawa S.,
Zienkiewicz O. C.,
Heinrich J. C.
Publication year - 1980
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620151111
Subject(s) - upwind scheme , dissipation , finite element method , mathematics , convection–diffusion equation , convection , discontinuous galerkin method , petrov–galerkin method , mathematical analysis , mathematical optimization , mechanics , physics , discretization , thermodynamics
In one dimension, Petrov—Galerkin nonsymmetric weighting for the convective diffusion equation can be interpreted as an added dissipation. The addition of an appropriate amount of dissipation can therefore give the same oscillation‐free solutions as the ‘unwinding’, Petrov—Galerkin, finite element methods. The ‘balancing dissipation’ is optimally chosen so that excessive dissipation does not occur. A scheme is presented for extending this approach to two‐dimensional problems, and numerical examples show that the new method can be used with improved computational efficiency.