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Relaxation of vectorial variational problems

Tomáš Roubíček (1995)

Mathematica Bohemica

Multidimensional vectorial non-quasiconvex variational problems are relaxed by means of a generalized-Young-functional technique. Selective first-order optimality conditions, having the form of an Euler-Weiestrass condition involving minors, are formulated in a special, rather a model case when the potential has a polyconvex quasiconvexification.

Reliable computation and local mesh adaptivity in limit analysis

Sysala, Stanislav, Haslinger, Jaroslav, Repin, Sergey (2019)

Programs and Algorithms of Numerical Mathematics

The contribution is devoted to computations of the limit load for a perfectly plastic model with the von Mises yield criterion. The limit factor of a prescribed load is defined by a specific variational problem, the so-called limit analysis problem. This problem is solved in terms of deformation fields by a penalization, the finite element and the semismooth Newton methods. From the numerical solution, we derive a guaranteed upper bound of the limit factor. To achieve more accurate results, a local...

Residual a posteriori error estimators for contact problems in elasticity

Patrick Hild, Serge Nicaise (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the unilateral contact problem in linear elasticity. We define two a posteriori error estimators of residual type to evaluate the accuracy of the mixed finite element approximation of the contact problem. Upper and lower bounds of the discretization error are proved for both estimators and several computations are performed to illustrate the theoretical results.

Resolution of the time dependent Pn equations by a Godunov type scheme having the diffusion limit

Patricia Cargo, Gérald Samba (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the Pn model to approximate the time dependent transport equation in one dimension of space. In a diffusive regime, the solution of this system is solution of a diffusion equation. We are looking for a numerical scheme having the diffusion limit property: in a diffusive regime, it has to give the solution of the limiting diffusion equation on a mesh at the diffusion scale. The numerical scheme proposed is an extension of the Godunov type scheme proposed by Gosse to solve the P1 model...

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