WIAS Preprint No. 2237, (2016)

On the uniqueness and numerical approximation of solutions to certain parabolic quasi-variational inequalities



Authors

  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Rautenberg, Carlos N.
    ORCID: 0000-0001-9497-9296

2010 Mathematics Subject Classification

  • 47J20 49J40 49M15 65J15 65K10

Keywords

  • Quasi-variational inequality, gradient constraints, obstacle problem, semismooth Newton method

Abstract

A class of abstract nonlinear evolution quasi-variational inequality (QVI) problems in function space is considered. The abstract framework developed in this paper includes constraint sets of obstacle and gradient type. The paper address the existence, uniqueness and approximation of solutions when the constraint set mapping is of a special form. Uniqueness is addressed through contractive behavior of a nonlinear mapping whose fixed points are solutions to the QVI. An axiomatic semi-discrete approximation scheme is developed, which is proven to be convergent and which is numerically implemented. The paper ends by a report on numerical tests for several nonlinear constraints of gradient-type.

Appeared in

  • Port. Math., 74 (2017), pp. 1--35.

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