Adaptive Nonconforming Finite Element Approximation of Eigenvalue Clusters
نویسنده
چکیده
This paper analyses an adaptive nonconforming finite element method for eigenvalue clusters of self-adjoint operators and proves optimal convergence rates (with respect to the concept of nonlinear approximation classes) for the approximation of the invariant subspace spanned by the eigenfunctions of the eigenvalue cluster. Applications include eigenvalues of the Laplacian and of the Stokes system.
منابع مشابه
A Type of Multi-level Correction Method for Eigenvalue Problems by Nonconforming Finite Element Methods
In this paper, a type of multi-level correction scheme is proposed to solve eigenvalue problems by the nonconforming finite element method. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an eigenvalue problem on the coarsest finite element space. This correctio...
متن کاملA Multilevel Correction Method for Steklov Eigenvalue Problem by Nonconforming Finite Element Methods
In this paper, a multilevel correction scheme is proposed to solve the Steklov eigenvalue problem by nonconforming finite element methods. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an Steklov eigenvalue problem on the coarsest finite element space. This co...
متن کاملA Posteriori Error Analysis for Nonconforming Approximation of Multiple Eigenvalues
In this paper we study an a posteriori error indicator introduced in E. Dari, R.G. Durán, C. Padra, Appl. Numer. Math., 2012, for the approximation of Laplace eigenvalue problem with Crouzeix–Raviart non-conforming finite elements. In particular, we show that the estimator is robust also in presence of eigenvalues of multiplicity greater than one. Some numerical examples confirm the theory and ...
متن کاملExtrapolation of Mixed Finite Element Approximations for the Maxwell Eigenvalue Problem
In this paper, a general method to derive asymptotic error expansion formulas for the mixed finite element approximations of the Maxwell eigenvalue problem is established. Abstract lemmas for the error of the eigenvalue approximations are obtained. Based on the asymptotic error expansion formulas, the Richardson extrapolation method is employed to improve the accuracy of the approximations for ...
متن کاملNonconforming finite element approximations of the Steklov eigenvalue problem
Article history: Received 27 November 2008 Received in revised form 27 March 2009 Accepted 22 April 2009 Available online 3 May 2009 MSC: 65N25 65N30 65N15
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Comput. Meth. in Appl. Math.
دوره 14 شماره
صفحات -
تاریخ انتشار 2014