Abstract. Semilinear elliptic optimal control problems involving the L1 norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for piecewise constant discretizations for the control and piecewise linear discretizations of the state are shown. Error estimates for the variational discret...

The symmetric coupling of mixed nite element and boundary element methods is analysed for a model interface problem with the Laplacian. The coupling involves a further continuous ansatz function on the interface to link the discontinuous displacement eld to the necessarily continuous boundary ansatz function. Quasi-optimal a priori error estimates and sharp a posteriori error estimates are esta...

Abstract In this paper we discuss spectral properties of operators associated with the least-squares finite-element approximation elliptic partial differential equations. The convergence discrete eigenvalues and eigenfunctions towards corresponding continuous eigenmodes is studied analyzed help appropriate $L^2$ error estimates. A priori a posteriori estimates are proved.

We study the problem -? u = f , where has a point-singularity. In particular, we are interested in ? x 0 Dirac delta with support but singularities of form ~ | ? ?s also considered. prove stability Galerkin projection on graded meshes weighted spaces, weights given by powers distance to . recover optimal rates convergence for finite element method these meshes. Our approach is general and holds...