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interpolation estimate

N. Sukumar's picture

Gradient bounds for Wachspress shape functions on polytopes

In this contribution (see, we derive lower and upper bounds for Wachspress coordinates over any simple d-dimensional simple convex polytope.  Numerical results for the Poisson equation on nontrivial polyhedral meshes are presented that affirm the linear rate of convergence in the energy seminorm of the polyhedral finite element method.  Matlab code to compute the Wachspress shape functions and its gradient on convex polygonal and polyhedral elements is also provided.

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