Zugl.: Marburg, Univ., Diss., 2007

Zugl.: Kaiserslautern, Techn. University, Diss., 2006.

Chemnitz, Techn. Univ., Diplomarb., 2003.

Zugl.: Bremen, Universiẗat, Diss.

München, Techn. Univ., Diss., 2005.

Augsburg, Univ., Diss., 2007.

Universiẗat, Diss., 2003--Kiel.

University, Diss., 2003--Tübingen.

The development of adaptive finite element procedures for the solution of geometrically and physically nonlinear problems in structural mechanics is very important for the augmentation of the efficiency of FE-codes. In this contribution methods of mesh refinement as well as mesh coarsening are presented for a material model considering finite elasto-plastic deformations. For newly generated elements stresses, strains and internal variables have to be calculated. This implies the determination of the nodal values as well as the Gaussian point values of the new elements based on the transfer of data from the former mesh. Analogously, the coarsening of less important elements necessitates the determination of these values for the newly created father elements.

We present an $hp$-adaptive strategy that is based on estimating the decay of the expansion coefficients when a function is expanded in $L^2$-orthogonal polynomails on a triangle or a tetrahedron. This method is justified by showing that the decay of the coefficients is exponential if and only if the function is analytic. Numerical examples illustrate the performance of this approach, and we compare it with two other $hp$-adaptive strategies.