Higher-order adaptive FEM for non-linear coupled problems
Abstract
The hp-FEM is a modern version of the Finite Element Method (FEM) which combines elements of variable diameter h and polynomial degree p to obtain extremely fast (exponential) convergence rates. In this thesis we develop new algorithms for the treatment of arbitrary-level hanging nodes in the hp-FEM, which allows us to design new automatic hp-adaptivity algorithms that are simpler but at the same time more efficient than the best automatic hp-adaptive strategies which are available today, as demonstrated on benchmark problems. A new multi-mesh assembling technology for efficient solution of coupled problems is presented. The algorithms are implemented in the form of a new highly modular hp-FEM system. The performance of the code is demonstrated on several real-life engineering problems, including a model of electrostatic micromotor and the Girkmann problem of linear elasticity.
Subject Area
Mathematics
Recommended Citation
Cerveny, Jakub, "Higher-order adaptive FEM for non-linear coupled problems" (2007). ETD Collection for University of Texas, El Paso. AAI1445681.
https://scholarworks.utep.edu/dissertations/AAI1445681