A convergent adaptive finite element method for the primal problem of elastoplasticity

A Convergent Adaptive Finite Element Method for the Primal Problem of Elastoplasticity

The boundary value problem representing one time step of the primal formulation of elastoplasticity with positive hardening leads to a variational inequality of the second kind with some non-differentiable functional. This paper establishes an adaptive finite element algorithm for the solution of this variational inequality that yields the energy reduction and, up to higher order terms, the R−l...

A Convergent Adaptive Uzawa Finite Element Method for the Nonlinear Stokes Problem

A convergent adaptive finite element method for an optimal design problem

Abstract. The optimal design problem for maximal torsion stiffness of an infinite bar of given geometry and unknown distribution of two materials of prescribed amounts is one model example in topology optimisation. It eventually leads to a degenerated convex minimisation problem. The numerical analysis is therefore delicate for possibly multiple primal variables u but unique derivatives σ := DW...

A convergent finite element method with adaptive √ 3 refinement

We develop an adaptive finite element method (AFEM) using piecewise linears on a sequence of triangulations obtained by adaptive √ 3 refinement. The motivation to consider √ 3 refinement stems from the fact that it is a slower topological refinement than the usual red or red-green refinement, and that it alternates the orientation of the refined triangles, such that certain features or singular...

A convergent adaptive finite element method with optimal complexity

In this paper, we introduce and analyze a simple adaptive finite element method for second order elliptic partial differential equations. The marking strategy depends on whether the data oscillation is sufficiently small compared to the error estimator in the current mesh. If the oscillation is small compared to the error estimator, we mark as many edges such that their contributions to the loc...