Mixed finite element approximation of the vector potential |
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Authors: | Rüdiger Verfürth |
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Institution: | (1) Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293, D-6900 Heidelberg, Federal Republic of Germany |
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Abstract: | Summary We consider a mixed finite element approximation of the three dimensional vector potential, which plays an important rôle in the simulation of perfect fluids and in the calculation of rotational corrections to transonic potential flows. The central point of our approach is a saddlepoint formulation of the essential boundary conditions. In particular, this avoids the wellknown Babu ka paradox when approximating smooth domains by polyhedrons. Using piecewise linear/piecewise constant elements for the vector potential/the boundary terms, we obtain optimal error estimates under minimal regularity assumptions for the solution of the continuous problem. |
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Keywords: | AMS(MOS): 65N30 CR: G1 8 |
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