Goal-oriented error estimation and adaptive mesh refinement in dynamic coupled thermoelasticity

• AMR for dynamic coupled thermoelasticity problems based on GOEE is presented.
• SPR, L2L2-PR and WSPR methods are used to estimate the error in the QoI.
• WSPR predicts the error more accurate and effective than SPR and L2L2-PR methods.

We present an adaptive method for dynamic coupled thermoelasticity problems based on goal-oriented error estimation. We use dimensionless variables in the finite element formulation and for the time integration we employ the acceleration-based Newmark method. Different recovery methods such as superconvergent patch recovery (SPR), L2L2-projection patch recovery (L2L2-PR) and weighted superconvergent patch recovery (WSPR) are used to estimate the error in the quantity of interest (QoI). By using adaptive refinement in space, the error in the quantity of interest is minimized. Therefore, the discretization is refined such that the error is equally distributed on the refined mesh. We demonstrate the efficiency of this method by numerous numerical examples.