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A stable Petrov-Galerkin method for convection-dominated problems

✍ Scribed by Regina C. Almeida; Renato S. Silva

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
1004 KB
Volume
140
Category
Article
ISSN
0045-7825

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✦ Synopsis

In this paper, a new Petrov-Galerkin formulation for solving convection-dominated problems is presented. The method developed achieves the quasi-optimal convergence rates when the solution is regular and provides the necessary stability to avoid spurious oscillations when strong gradients are present. Such important properties allow the use of p refinement to improve the solution in regions with discontinuities because of the stability engendered by the new Petrov-Galerkin method. In this matter, a proper evaluation of the intrinsic time scale function, appearing in the design of this method, is crucial to guarantee the required accuracy.

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## Abstract In this work, a stable Petrov–Galerkin formulation is combined with an __hp__‐adaptive refinement strategy. The stability engendered by this formulation allows the use of high interpolation element order in regions with steep gradients. The new __hp__‐adaptive strategy, originally propo