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Interpolation Operator on negative Sobolev Spaces

Lars DieningJohannes StornTabea Tscherpel
摘要
We introduce a Scott--Zhang type projection operator mapping to Lagrangeelements for arbitrary polynomial order. In addition to the usual properties,this operator is compatible with duals of first order Sobolev spaces. Morespecifically, it is stable in the corresponding negative norms and allows foroptimal rates of convergence. We discuss alternative operators with similarproperties. As applications of the operator we prove interpolation errorestimates for parabolic problems and smoothen rough right-hand sides in a leastsquares finite element method.
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