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Improvement of MacCormack's scheme for Burgers' equation. Using a finite element method
Author(s) -
Lucchi Ciro 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.1620150406
Subject(s) - finite element method , mathematics , divergence (linguistics) , discretization , mixed finite element method , extended finite element method , variable (mathematics) , scheme (mathematics) , mathematical analysis , engineering , structural engineering , philosophy , linguistics
A brief description of the finite element method to be used is given. It is then shown how various finite difference schemes for the wave and Burgers' equations can be achieved, in particular the predictor‐corrector method of MacCormack. By the finite element method a more efficient predictor‐corrector scheme is also obtained. Furthermore, the study tends to show that terms of the general form ∂(uvw)/∂x should be discretized by considering u,v and w as separate variables instead of taking the product uvw as a single variable as is often done with equations written in conservative (divergence law) form.