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Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials. (English) Zbl 0608.65013
The authors study the divergence operator acting on continuous piecewise polynomials of degree $$p+1$$, $$p\geq 3$$, over triangulations of a plane polygonal domain. A combinatorial argument is used to verify a characterization of the range of the divergence operator. It is shown that for every general families of meshes it is possible to find a maximal right inverse for the divergence operator with a $$B(L_ 2,H^ 1)$$ norm which is bounded independently of the mesh size. The norm of this right inverse grows at most algebraically with p, but it necessarily blows up as a certain measure of singularity of the meshes approaches 0.
Reviewer: P.Narain

##### MSC:
 65D25 Numerical differentiation 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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##### References:
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