A theory for local, a posteriori, pointwise, residual-based estimation of the finite element error

Local , a Posteriori , Pointwise , Residual Basedestimation of the Finite Element

Local , a Posteriori , Pointwise Estimationofthe Finite Element

When a boundary value problem has a classical solution, then the nite element error function is described by being the solution to a diierent boundary value problem. In this work such a boundary value problem for the error is developed, with boundary conditions of Dirichlet and Neumann type on the boundaries of all nite elements. The error problem is linear in the error, and contains non comput...

A Theory Forlocal , a Posteriori , Pointwise , Residual Basedestimation of the Finite Element

A posteriori error estimation of finite element approximations of pointwise state constrained distributed control problems

We provide an a posteriori error analysis of finite element approximations of pointwise state constrained distributed optimal control problems for second order elliptic boundary value problems. In particular, we derive a residual-type a posteriori error estimator and prove its efficiency and reliability up to oscillations in the data of the problem and a consistency error term. In contrast to t...

A Posteriori Finite Element Error Estimation for Diffusion Problems

Adjerid et al. 2] and Yu 19, 20] show that a posteriori estimates of spatial discretiza-tion errors of piecewise bi-p polynomial nite element solutions of elliptic and parabolic problems on meshes of square elements may be obtained from jumps in solution gradients at element vertices when p is odd and from local elliptic or parabolic problems when p is even. We show that these simple error esti...