Hybrid finite elements for nonlinear thermal and hygral problems

Abstract

The performance of a hybrid finite element formulation developed for the solution of nonlinear transient problems is assessed. The formulation, already applied to the solution of heat transfer and moisture transport problems, develops from the uncoupling of the approximation of the state variables and the mapping of the geometry. The formulation qualifies as hybrid because the state variable and its gradient are approximated independently. Orthogonal bases are used to enhance numerical stability under high-order approximations. The resulting solving system is highly sparse and well-suited to adaptive refinement and parallel processing. Besides the benchmarks used in the assessment of conform elements, the rates and patterns of convergence of the hybrid element are defined and its sensitivity to shape distortion is analysed. Also illustrated is the simulation of singular heat flow fields in cracked plates and the hygro-thermo-chemical modelling of cement hydration in concrete structures.