Rüdiger Verfürth

A posteriori error estimators for the Stokes equations

SummaryWe present two a posteriori error estimators for the mini-element discretization of the Stokes equations. One is based on a suitable evaluation of the residual of the finite element solution. The other one is based on the solution of suitable local Stokes problems involving the residual of the finite element solution. Both estimators are globally upper and locally lower bounds for the error of the finite element discretization. Numerical examples show their efficiency both in estimating the error and in controlling an automatic, self-adaptive mesh-refinement process. The methods presented here can easily be generalized to the Navier-Stokes equations and to other discretization schemes.

A posteriori error estimation and adaptive mesh-refinement techniques

Introduction. A Simple Model Problem. Abstract Nonlinear Equations. Finite Element Discretizations of Elliptic PDEs. Practical Implementation. Bibliography. Subject Index.

A posteriori error estimators for convection-diffusion equations

Summary. We derive a posteriori error estimators for convection-diffusion equations with dominant convection. The estimators yield global upper and local lower bounds on the error measured in the energy norm such that the ratio of the upper and lower bounds only depends on the local mesh-Peclet number. The estimators are either based on the evaluation of local residuals or on the solution of discrete local Dirichlet or Neumann problems.

Edge Residuals Dominate A Posteriori Error Estimates for Low Order Finite Element Methods

We prove that, up to higher order perturbation terms, edge residuals yield global upper and local lower bounds on the error of linear finite element methods both in H1- and L2-norms. We present two proofs: one uses the standard L2-projection and the other relies on a new, weighted Clement-type interpolation operator.

A Posteriori Error Estimators for the Raviart--Thomas Element

When error estimators for the \RTe\ are developed, two difficulties prevent the success of the straightforward application of frequently used arguments. The

A posteriori error estimation techniques for finite element methods

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Analysis of a streamline diffusion finite element method for the Stokes and Navier-Stokes equations

-norm is an anisotropic norm; i.e., it refers to differential operators of different orders. Moreover, the traces of

Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition

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A review of a posteriori error estimation techniques for elasticity problems

-functions are only in

Robust A Posteriori Error Estimates for Stationary Convection-Diffusion Equations

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