PUB - Publikationen an der Universität Bielefeld

We develop a discrete counterpart of the De Giorgi-Nash-Moser theory, which provides uniform Holder-norm bounds on continuous piecewise affine finite element approximations of second-order linear elliptic problems of the form -del center dot (A del u) = f - del center dot F with A epsilon L-infinity (Omega; R-nxn) a uniformly elliptic matrix-valued function, f epsilon L-q(Omega), F epsilon L-p(Omega; R-n), with p > n and q > n/2, on A-nonobtuse shape-regular triangulations, which are not required to be quasi-uniform, of a bounded polyhedral Lipschitz domain Omega subset of R-n.