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

In linear thermoelasticity models, the temperature TT and the displacement components u1,u2u1,u2 exhibit large qualitative differences: while TT typically is very smooth everywhere in the domain, the displacements u1,u2u1,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. One of the best available methods for this task is the exponentially-convergent hphp-FEM. Note, however, that standard adaptive hphp-FEM approximates all three fields u1,u2u1,u2 and TT on the same mesh, and thus it treats TT as if it were singular at re-entrant corners as well. Therefore, a large number of degrees of freedom of temperature are wasted. This motivates us to approximate the fields u1,u2u1,u2 and TT on individual hphp-meshes equipped with mutually independent hphp-adaptivity mechanisms. In this paper we describe mathematical and algorithmic aspects of the novel adaptive multimesh hphp-FEM, and demonstrate numerically that it performs better than the standard adaptive hh-FEM and hphp-FEM.