Abstract
In this paper, for two second order elliptic boundary value problems, uniform convergence error estimates are derived using piecewise linear (conforming and non-conforming) finite elements. The estimates are valid for polyhedral convex regionsΩ ⊂Rn with 1≦n≦3. The proof of the estimates is mainly based on Sobolev's inequality, by which the uniform estimates are reduced to estimates in the mean. In this way, it is possible to obtain the desired uniformO(h2)-estimate in the plane as a special case, thus confirming theoretically Natterer's numerical results.
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