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


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