Error estimates of the lumped mass finite element method for semilinear elliptic problems

Some error estimates for the lumped mass finite element method for a parabolic problem

We study the spatially semidiscrete lumped mass method for the model homogeneous heat equation with homogeneous Dirichlet boundary conditions. Improving earlier results we show that known optimal order smooth initial data error estimates for the standard Galerkin method carry over to the lumped mass method whereas nonsmooth initial data estimates require special assumptions on the triangulation...

Error Estimates for Finite Element Approximations of Elliptic Control Problems

We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.

A posteriori error estimates for nonlinear problems. Lr-estimates for finite element discretizations of elliptic equations

— We extend the gênerai framework of [18] for deriving a posteriori error estimâtes for approximate solutions of noniinear elliptic problems such ihat it also yields L'-error estimâtes. The gênerai results are applied to finite element discretizations of scalar quasilinear elliptic pdes of 2nd order and the stationary incompressible Navier-Stokes équations. They immediately yield a posteriori e...

Error Estimates for a Semilinear Elliptic

A priori error estimates for space-time finite element discretization of semilinear parabolic optimal control problems

In this paper, a priori error estimates for space-time finite element discretizations of optimal control problems governed by semilinear parabolic PDEs and subject to pointwise control constraints are derived. We extend the approach from [23, 24], where linear-quadratic problems have been considered, discretizing the state equation by usual conforming finite elements in space and a discontinuou...