Sharp estimates for finite element approximations to elliptic problems with neumann boundary data of low regularity

摘要

Consider a second order homogeneous elliptic problem with smooth coefficients, Au = 0, on a smooth domain,., but with Neumann boundary data of low regularity. Interior maximum norm error estimates are given for C-o finite element approximations to this problem. When the Neumann data is not in L-1(partial derivative Omega), these local estimates are not of optimal order but are nevertheless shown to be sharp. A method for ameliorating this sub-optimality by preliminary smoothing of the boundary data is given. Numerical examples illustrate the findings.