Premium
Optimal finite element solutions to diffusion–convection problems in one dimension
Author(s) -
Barrett J. W.,
Morton K. W.
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.1620151004
Subject(s) - mathematics , superconvergence , bilinear interpolation , finite element method , galerkin method , space (punctuation) , diffusion , convection–diffusion equation , dimension (graph theory) , polygon mesh , convection , position (finance) , character (mathematics) , mathematical analysis , mathematical optimization , computer science , geometry , mechanics , physics , pure mathematics , statistics , finance , economics , thermodynamics , operating system
Petrov–Galerkin methods have been proposed by several authors to eliminate the inaccuracies and oscillations obtained with Galerkin methods when applied to diffusion–convection problems at high Péclet numbers: the difficulty is to select the appropriate test space for a given trial space. We investigate here choices of test space which either exactly or approximately symmetrize the associated bilinear form and so retain the optimal character of the approximate solution. This is the key to high accuracy and superconvergence, and optimal recovery techniques are proposed to obtain the maximum information from the approximations. Examples are given to show how the position and thickness of boundary layers may be estimated with relatively coarse meshes.