Abstract

Non-quasiconvex variational problems require, in general, a relaxation to ensure existence of their solutions. Here a relaxation by (generalized) Young functionals is used and then a finite-element method for a direct numerical approximation of the relaxed problems is developed. Beside a mere convergence, also some error estimates are analysed and a comparison with other methods is discussed.

Author information

Contact details are reproduced from the original publication and may be historical.

T. Roubíček

Mathematical Institute, Charles University, Sokolovská 83, CZ-186 00 Praha 8, and Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 4, CZ-182 08 Praha 8, Czech Republic.

Keywords

  • Vectorial variational problem
  • relaxation
  • generalized Young functionals
  • finite-element approximation

Suggested citation

T. Roubíček. “Numerical Approximation of Relaxed Variational Problems.” Journal of Convex Analysis 3 (1996), No. 2, 329–347. https://doi.org/10.68381/jca03022

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Published by Heldermann Verlag, 1996. Rights now held by Banach Press.