L2L^2-error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes

summary: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

Optimal control of the Stokes equations: conforming and non-conforming finite element methods under reduced regularity

PDE-constrained optimization, Control-constraints, Finite element method, Non-conforming elements, Anisotropic mesh-grading, A priori error estimates, Stokes equations,