A partition-of-unity-based variational localization of the dual-weighted residual estimator

Prof. Thomas Wick

Jan. 20, 2015, 3:30 p.m. S2 059

In this talk, we introduce a novel localization technique for the
dual-weighted residual (DWR) method for a posteriori error estimation and
mesh adaptivity. This new technique is based on the
introduction of a partition of unity and uses the
variational form; and is consequently very
easy to apply, as neither strong residuals nor jumps over element
edges are required. Such an approach is a great advantage for coupled
multiphysics problems because the strong from is neither available
or too expensive to evaluate.
In the mathematical analysis, we show for
different localization techniques (established methods and the
new one), that the local error indicators used for mesh adaptivity
converge with the proper order in the error functional.
As key applications, we have in mind to treat nonlinear solid mechanics and
multiphysics problems such as fluid-structure interaction.
Related numerical examples and standard tests are consulted to illustrate
our findings.