Robust Estimates for hp-Adaptive Approximations of Non-Self-Adjoint Eigenvalue Problems
نویسندگان
چکیده
We present new residual estimates based on Kato’s square root theorem for spectral approximations of non-self-adjoint differential operators of convection–diffusion–reaction type. These estimates are incorporated as part of an hp-adaptive finite element algorithm for practical spectral computations, where it is shown that the resulting a posteriori error estimates are reliable. Provided experiments demonstrate the efficiency and reliability of our approach.
منابع مشابه
A Posteriori and a Priori Error Analysis for Finite Element Approximations of Self-Adjoint Elliptic Eigenvalue Problems
We present a new error analysis for finite element approximations of self-adjoint elliptic eigenvalue problems. The analysis consists of three steps. First we prove a posteriori estimates for the error in the approximate eigenvectors and eigenvalues. The error in the eigenvectors is measured both in the L' and energy norms. In these estimates the error is bounded in terms of the mesh size, a st...
متن کاملAdaptive computation of smallest eigenvalues of self-adjoint elliptic partial differential equations
We consider a new adaptive finite element (AFEM) algorithm for self-adjoint elliptic PDE eigenvalue problems. In contrast to other approaches we incorporate the inexact solutions of the resulting finite dimensional algebraic eigenvalue problems into the adaptation process. In this way we can balance the costs of the adaptive refinement of the mesh with the costs for the iterative eigenvalue met...
متن کاملOn Rayleigh-Ritz Method in Three-Parameter Eigenvalue Problems
This paper deals with the computation of the eigenvalues of a three-parameter Sturm-Liouville problem in the form of ordinary differential equation using Rayleigh-Ritz Method, a method which is based on the principle of variational methods. This method has been effective in computing the eigenvalues of self-adjoint problems. The resulting equations obtained in applying Rayleigh-Ritz method on t...
متن کاملEquivalent a posteriori error estimates for spectral element solutions of constrained optimal control problem in one dimension
In this paper, we study spectral element approximation for a constrained optimal control problem in one dimension. The equivalent a posteriori error estimators are derived for the control, the state and the adjoint state approximation. Such estimators can be used to construct adaptive spectral elements for the control problems.
متن کاملGuaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations
This paper derives a posteriori error estimates for conforming numerical approximations of the Laplace eigenvalue problem with a homogeneous Dirichlet boundary condition. In particular, upper and lower bounds for an arbitrary simple eigenvalue are given. These bounds are guaranteed, fully computable, and converge with optimal speed to the given exact eigenvalue. They are valid without restricti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016