Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM
Mathematics and Computers in Simulation
Adaptive hp-FEM with dynamical meshes for transient heat and moisture transfer problems
Journal of Computational and Applied Mathematics
Journal of Computational Physics
An iterative adaptive finite element method for elliptic eigenvalue problems
Journal of Computational and Applied Mathematics
Solving a suite of NIST benchmark problems for adaptive FEM with the Hermes library
Journal of Computational and Applied Mathematics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
hp-FEM electromechanical transduction model of ionic polymer-metal composites
Journal of Computational and Applied Mathematics
Hi-index | 7.31 |
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 hp-FEM. Note, however, that standard adaptive hp-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 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 the standard adaptive h-FEM and hp-FEM.