Adventures in adaptivity

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• 作者：Randolph E. Bank ; Chris Deotte
• 关键词：h ; Adaptive ; hp ; Adaptive ; Finite elements ; A posteriori error estimation ; Interpolation ; Convergence order ; PDE
• 刊名：Computing and Visualization in Science
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：18
• 期：2-3
• 页码：79-91
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Computational Mathematics and Numerical Analysis; Computer Applications in Chemistry; Algorithms; Visualization; Numerical Analysis; Calculus of Variations and Optimal Control; Optimization;
• 出版者：Springer Berlin Heidelberg
• ISSN：1433-0369
• 卷排序：18

文摘

In this work, we compare and contrast a few finite element h-adaptive and hp-adaptive algorithms. We test these schemes on three example PDE problems and we utilize and evaluate an a posteriori error estimate. In the process, we introduce a new framework to study adaptive algorithms and a posteriori error estimators. Our innovative environment begins with a solution u and then uses interpolation to simulate solving a corresponding PDE. As a result, we always know the exact error and we avoid the noise associated with solving. Using an effort indicator, we evaluate the relationship between accuracy and computational work. We report the order of convergence of different approaches. And we evaluate the accuracy and effectiveness of an a posteriori error estimator.