Displaying similar documents to “Sharp upper global a posteriori error estimates for nonlinear elliptic variational problems”

Verification of functional a posteriori error estimates for obstacle problem in 1D

Petr Harasim, Jan Valdman (2013)

Kybernetika

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We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed. ...

L 2 -error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes

Thomas Apel, Dieter Sirch (2011)

Applications of Mathematics

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An L 2 -estimate of the finite element error is proved for a Dirichlet and a Neumann boundary value problem on a three-dimensional, prismatic and non-convex domain that is discretized by an anisotropic tetrahedral mesh. To this end, an approximation error estimate for an interpolation operator that is preserving the Dirichlet boundary conditions is given. The challenge for the Neumann problem is the proof of a local interpolation error estimate for functions from a weighted Sobolev space. ...

A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems

Torsten Linß (2014)

Applications of Mathematics

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FEM discretizations of arbitrary order r are considered for a singularly perturbed one-dimensional reaction-diffusion problem whose solution exhibits strong layers. A posteriori error bounds of interpolation type are derived in the maximum norm. An adaptive algorithm is devised to resolve the boundary layers. Numerical experiments complement our theoretical results.

Superconvergence analysis and a posteriori error estimation of a Finite Element Method for an optimal control problem governed by integral equations

Ningning Yan (2009)

Applications of Mathematics

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In this paper, we discuss the numerical simulation for a class of constrained optimal control problems governed by integral equations. The Galerkin method is used for the approximation of the problem. A priori error estimates and a superconvergence analysis for the approximation scheme are presented. Based on the results of the superconvergence analysis, a recovery type a posteriori error estimator is provided, which can be used for adaptive mesh refinement.