Monolithic discretization of linear thermoelasticity problems via adaptive multimesh hp-FEM

In linear thermoelasticity models, the temperature T and the displacement components u1, u2 exhibit large qualitative differences: While T typically is very smooth everywhere in the domain, the displacements u1, u2 have singular gradients (stresses) at re-entrant corners and edges. The mesh must be extremely fine in these areas so that stress intensity factors are resolved sufficiently. Among the best available methods for this task is the exponentially-convergent hp-FEM. Note, however, that standard adaptive hp-FEM approximates all three fields u1, u2 and T on the same mesh, and thus it treats T as if it was singular at re-entrant corners as well. Therefore, large numbers of temperature degrees of freedom are wasted. This motivates us to approximate the fields u1, u2 and T on individual hp-meshes equipped with mutually independent hp-adaptivity mechanisms. In this paper we describe mathematical and algorithmic aspects of the novel adaptive multimesh hp-FEM, and demonstrate numerically that it performs better than standard adaptive h-FEM and hp-FEM.