Adaptive thermo-mechanical finite element formulation based on goal-oriented error estimation

In this paper, a rh-adaptive thermo-mechanical formulation based on goal-oriented error estimation is proposed. The goal-oriented error estimation relies on different recovery-based error estimators, i.e. the superconvergent patch recovery (SPR), L2-projection patch recovery (L2-PR) and weighted superconvergent patch recovery (WSPR). A new adaptive refinement strategy (ARS) is presented that minimizes the error in a quantity of interest and refines the discretization such that the error is equally distributed on the refined mesh. The method is validated by numerous numerical examples where an analytical solution or reference solution is available.