Saddle-point problems with bilinear Lagrangian and convex constraints: analysis, numerical solution and applications

Abstract: The first part of the talk is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. The conditions that guarantee no gap between the inf-sup and related sup-inf problems are studied. A particular attention is devoted to the inf-sup condition defined for convex cones in function spaces. Next, a regularization method convenient for solving the inf-sup problem is analyzed and a computable majorant of the critical (inf-sup) value is derived for purposes of a posteriori error analysis of numerical results. The second part of the talk is devoted to applications of the abstract framework to continuum mechanics. In particular, examples of limit load problems and similar ones arising in classical plasticity, gradient plasticity and delamination are introduced. The presented results follow from the joint work with Daya B. Reddy, Sergey Repin and Jaroslav Haslinger.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).