hp-Adaptive composite discontinuous Galerkin methods for elliptic eigenvalue problems on complicated domains

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• 作者：Stefano Giani ^{stefano.giani@durham.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Multi-level method ; Eigenvalue problem ; hp-Adaptivity ; Discontinuous Galerkin ; A posteriori error estimator
• 刊名：Applied Mathematics and Computation
• 出版年：2015
• 出版时间：15 September 2015
• 年：2015
• 卷：267
• 期：Complete
• 页码：604-617
• 全文大小：2665 K

文摘

In this paper we develop the a posteriori error estimation of hp-adaptive discontinuous Galerkin composite finite element methods (DGFEMs) for the discretization of second-order elliptic eigenvalue problems. DGFEMs allow for the approximation of problems posed on computational domains which may contain local geometric features. The dimension of the composite finite element space is independent of the number of geometric features. This is in contrast with standard finite element methods, as the minimal number of elements needed to represent the underlying domain can be very large and so the dimension of the finite element space. Computable upper bounds on the error for both eigenvalues and eigenfunctions are derived. Numerical experiments highlighting the practical application of the proposed estimators within an automatic hp-adaptive refinement procedure will be presented.