Convergence and quasi-optimal complexity of a simple adaptive finite element method
نویسندگان
چکیده
منابع مشابه
Convergence and Quasi-optimal Complexity of a Simple Adaptive Finite Element Method
We prove convergence and quasi-optimal complexity of an adaptive finite element algorithm on triangular meshes with standard mesh refinement. Our algorithm is based on an adaptive marking strategy. In each iteration, a simple edge estimator is compared to an oscillation term and the marking of cells for refinement is done according to the dominant contribution only. In addition, we introduce an...
متن کاملQuasi-Optimal Convergence Rate for an Adaptive Finite Element Method
We analyze the simplest and most standard adaptive finite element method (AFEM), with any polynomial degree, for general second order linear, symmetric elliptic operators. As is customary in practice, the AFEM marks exclusively according to the error estimator and performs a minimal element refinement without the interior node property. We prove that the AFEM is a contraction, for the sum of th...
متن کاملConvergence Rate and Quasi-Optimal Complexity of Adaptive Finite Element Computations for Multiple Eigenvalues
In this paper, we study an adaptive finite element method for multiple eigenvalue problems. We obtain both convergence rate and quasi-optimal complexity of the adaptive finite element eigenvalue approximation, without any additional assumption to those required in the adaptive finite element analysis for the boundary value problem. Our analysis is based on a certain relationship between the fin...
متن کاملQuasi-optimal Convergence Rate for an Adaptive Boundary Element Method
For the simple layer potential V that is associated with the 3D Laplacian, we consider the weakly singular integral equation V φ = f . This equation is discretized by the lowest order Galerkin boundary element method. We prove convergence of an h-adaptive algorithm that is driven by a weighted residual error estimator. Moreover, we identify the approximation class for which the adaptive algorit...
متن کاملConvergence of a Simple Adaptive Finite Element Method for Optimal Control
We prove convergence and optimal complexity of an adaptive finite element algorithm for a model problem of optimal control. Following previous work, our algorithm is based on an adaptive marking strategy which compares a simple edge estimator with an oscillation term in each step of the algorithm in order to adapt the marking of cells.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Mathematical Modelling and Numerical Analysis
سال: 2009
ISSN: 0764-583X,1290-3841
DOI: 10.1051/m2an/2009036