Numerische Mathematik

, Volume 50, Issue 6, pp 685–695

Mixed finite element approximation of the vector potential

  • Rüdiger Verfürth
On the Numerical Solution of the First Biharmonic Boundary Value Problem

DOI: 10.1007/BF01398379

Cite this article as:
Verfürth, R. Numer. Math. (1986) 50: 685. doi:10.1007/BF01398379


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 Babuška 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.

Subject Classifications

AMS(MOS): 65N30 CR: G1.8 

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Rüdiger Verfürth
    • 1
  1. 1.Institut für Angewandte MathematikUniversität HeidelbergHeidelbergFederal Republic of Germany

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