Averaging Techniques Yield Reliable Error Control in Fem Part I
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Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM
Averaging techniques are popular tools in adaptive finite element methods for the numerical treatment of second order partial differential equations since they provide efficient a posteriori error estimates by a simple post-processing. In this paper, their reliablility is shown for conforming, noncon-forming, and mixed low order finite element methods in a model situation: the Laplace equation ...
متن کاملEach averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM
Averaging techniques are popular tools in adaptive finite element methods since they provide efficient a posteriori error estimates by a simple postprocessing. In the second paper of our analysis of their reliability, we consider conforming h-FEM of higher (i.e., not of lowest) order in two or three space dimensions. In this paper, reliablility is shown for conforming higher order finite elemen...
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The reliability of frequently applied averaging techniques for a posteriori error control has recently been established for a series of nite element methods in the context of second-order partial diierential equations. This paper establishes related reliable and eecient a posteriori error estimates for the energy-norm error of an obstacle problem on unstructured grids as a model example for var...
متن کاملData Oscillation and Convergence of Adaptive FEM
Data oscillation is intrinsic information missed by the averaging process associated with nite element methods (FEM) regardless of quadra-ture. Ensuring a reduction rate of data oscillation, together with an error reduction based on a posteriori error estimators, we construct a simple and eecient adaptive FEM for elliptic PDE with linear rate of convergence without any preliminary mesh adaptati...
متن کاملAveraging Techniques for Reliable and Efficient A Posteriori Finite Element Error Control: Analysis and Applications
Local averaging techniques, which are used to postprocess discrete flux or stress approximations of low-order finite element schemes for elliptic boundary value problems, are applied for error control and adaptive mesh refinement. We put particular emphasis on the explicit calculation of all constants, arising in the proofs of reliability and efficiency, in terms of the known data and quantify ...
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تاریخ انتشار 1999