Benchmark results for testing adaptive finite element eigenvalue procedures part 2 (conforming eigenvector and eigenvalue estimates)

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• 作者：Stefano Giani^a ; ^{stefano.giani@nottingham.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Luka Grubi&scaron ; ić^b ; ^{luka.grubisic@math.hr" class="auth_mail" title="E-mail the corresponding author} ; Jeffrey S. Ovall^c ; ^{jovall@pdx.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Eigenvalue problems ; Finite element methods ; A posteriori error estimates ; hp-Adaptivity
• 刊名：Applied Numerical Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：102
• 期：Complete
• 页码：1-16
• 全文大小：1451 K

文摘

We present an hp-adaptive continuous Galerkin (hp-CG) method for approximating eigenvalues of elliptic operators, and demonstrate its utility on a collection of benchmark problems having features seen in many important practical applications—for example, high-contrast discontinuous coefficients giving rise to eigenfunctions with reduced regularity. In this continuation of our benchmark study, we concentrate on providing reliability estimates for assessing eigenfunction/invariant subspace error. In particular, we use these estimates to justify the observed robustness of eigenvalue error estimates in the presence of repeated or clustered eigenvalues. We also indicate a means for obtaining efficiency estimates from the available efficiency estimates for the associated boundary value (source) problem. As in the first part of the paper we provide extensive numerical tests for comparison with other high-order methods and also extend the list of analyzed benchmark problems.