Monolithic discretization of linear thermoelasticity problems via adaptive multimesh [formula omitted]-FEM

Abstract

In linear thermoelasticity models, the temperature T and the displacement components u 1 , u 2 exhibit large qualitative differences: while T typically is very smooth everywhere in the domain, the displacements u 1 , u 2 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 h p -FEM. Note, however, that standard adaptive h p -FEM approximates all three fields u 1 , u 2 and T on the same mesh, and thus it treats T 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 u 1 , u 2 and T on individual h p -meshes equipped with mutually independent h p -adaptivity mechanisms. In this paper we describe mathematical and algorithmic aspects of the novel adaptive multimesh h p -FEM, and demonstrate numerically that it performs better than the standard adaptive h -FEM and h p -FEM.