Balancing truncation and round-off errors in FEM: One-dimensional analysis

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:386

Article

Liu, Jie¹  Moller, Matthias¹  Schuttelaars, Henk M.¹ 

[1] Delft Univ Technol, Delft Inst Appl Math, Van Mourik Broekmanweg 6, NL-2628 XE Delft, Netherlands

关键词: Finite element method;    A posteriori error estimation;    Optimal number of degrees of freedom;    hp-refinement strategy;    Round-off error;   

DOI  :  10.1016/j.cam.2020.113219

来源: Elsevier

【 摘 要 】

In finite element methods, the accuracy of the solution cannot increase indefinitely since the round-off error related to limited computer precision increases when the number of degrees of freedom (DoFs) is large enough. Because a priori information of the highest attainable accuracy is of great interest, we construct an innovative method to obtain the highest attainable accuracy given the order of the elements. In this method, the truncation error is extrapolated when it converges at the asymptotic rate, and the bound of the round-off error follows from a generically valid error estimate, obtained and validated through extensive numerical experiments. The highest attainable accuracy is obtained by minimizing the sum of these two types of errors. We validate this method using a one-dimensional Helmholtz equation in space. It shows that the highest attainable accuracy can be accurately predicted, and the CPU time required is much smaller compared with that using successive grid refinement. (C) 2020 The Author(s). Published by Elsevier B.V.

【 授权许可】

Free