Efficiency-based hp-refinement for finite element methods

adaptive refinement;finite element methods;hp-refinement;Applied Mathematics

Tang, Lei

University of Waterloo

关键词: adaptive refinement;    finite element methods;    hp-refinement;    Applied Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/3178/1/ltang2007.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Two efficiency-based grid refinement strategies are investigated for adaptive finite elementsolution of partial differential equations. In each refinement step, the elements are orderedin terms of decreasing local error, and the optimal fraction of elements to be refined is deter-mined based on e±ciency measures that take both error reduction and work into account.The goal is to reach a pre-specified bound on the global error with a minimal amount ofwork. Two efficiency measures are discussed, ;;work times error;; and ;;accuracy per computational cost;;. The resulting refinement strategies are first compared for a one-dimensionalmodel problem that may have a singularity. Modified versions of the efficiency strategiesare proposed for the singular case, and the resulting adaptive methods are compared with athreshold-based refinement strategy. Next, the efficiency strategies are applied to the caseof hp-refinement for the one-dimensional model problem. The use of the efficiency-basedrefinement strategies is then explored for problems with spatial dimension greater thanone. The work times error strategy is inefficient when the spatial dimension, d, is largerthan the finite element order, p, but the accuracy per computational cost strategy providesan efficient refinement mechanism for any combination of d and p.