Dissipative and non-dissipative evolutionary quasi-variational inequalities with gradient constraints
- Hintermüller, Michael
- Rautenberg, Carlos N.
- Strogies, Nikolai
2010 Mathematics Subject Classification
- 35K86 47J20 49J40 49M15 65J15 65K10
- Quasi-variational inequality, gradient constraint, dissipative and non-dissipative processes, variable splitting solver
Evolutionary quasi-variational inequality (QVI) problems of dissipative and non-dissipative nature with pointwise constraints on the gradient are studied. A semi-discretization in time is employed for the study of the problems and the derivation of a numerical solution scheme, respectively. Convergence of the discretization procedure is proven and properties of the original infinite dimensional problem, such as existence, extra regularity and non-decrease in time, are derived. The proposed numerical solver reduces to a finite number of gradient-constrained convex optimization problems which can be solved rather efficiently. The paper ends with a report on numerical tests obtained by a variable splitting algorithm involving different nonlinearities and types of constraints.
- Set-Valued Var. Anal., 27 (2019), pp. 433--468 (published online on 14.07.2018), DOI 10.1007/s11228-018-0489-0 .