The Hp-Adaptive Finite Element Method For Three Dimensional Multiphysics - Kamaludin, Siti Sarah (2014)
Although the hp-adaptive strategy is well implemented in two dimensional problems, its convergence performance in three-dimensional multiphysics problems particularly with tetrahedral mesh is still yet to be fully matured. This thesis presents a code development of a fully automatic hp-adaptive finite element method for steady-state multi physics problems in three dimensions. The adaptivity is achieved by a systematic combination of mesh refinements using bisecting approach(/Z) and polynomial order(p) extensions of the approximation functions. Mesh adaptation process is implemented such that conformity among the elements is preserved. The adaptive strategy is driven by a residual-based a posteriori error estimator computed element-wise, where a scheme has been developed to identify elements that need to undergo refinement processes.