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Variable upwinding and adaptive mesh refinement in convection‐diffusion
Author(s) -
Carey G. F.,
Plover T.
Publication year - 1983
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.1620190304
Subject(s) - upwind scheme , convection–diffusion equation , polygon mesh , mathematics , numerical diffusion , variable (mathematics) , mesh generation , finite element method , convection , nonlinear system , steady state (chemistry) , adaptive mesh refinement , diffusion , mechanics , mathematical analysis , geometry , physics , thermodynamics , discretization , chemistry , computational science , quantum mechanics
An analysis of the stability and oscillation properties of upwind finite element methods for convection‐diffusion is given and used to develop a variable upwinding formulation. This formulation is particularly well suited to problems with nonconstant coefficients, nonlinearity or non‐uniform meshes. We present the theoretical analysis and numerical studies for a standard steady‐state and transient model one‐dimensional convection‐diffusion problem. The variable upwind strategy can also be used to significant advantage in conjunction with adaptive mesh refinement. Numerical results for the steady‐state case in which convection dominates and the mesh is adaptively refined into a boundary layer confirm the efficacy of the scheme.