Interpolation theory over curved elements, with applications to finite element methods

@inproceedings{Ciarlet1972InterpolationTO,
  title={Interpolation theory over curved elements, with applications to finite element methods},
  author={Philippe G. Ciarlet and P. A. Raviart},
  year={1972}
}
Abstract As is well known, an essential step in obtaining orders of convergence for finite element methods is an approximation theory problem: Given a finite element K and given a smooth function u defined over the set K , estimate ∥ u − Πu ∥ Hm ( K ) ' where П u is an interpolate of the function u defined over the set K , and ∥−∥ Hm ( K ) denotes the usual Sobolev norm. In this paper we develop a general theory for obtaining asymptotic estimates of the form ∥ u − Πu ∥ Hm ( K ) = O ( h k +1− m… CONTINUE READING

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