Simplified convergence proof in Bézier finite elements on D-dimensional simplex
arXiv:1801.10210h-index: 7
Originality Synthesis-oriented
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This is an incremental theoretical contribution for mathematicians working on approximation theory in higher dimensions.
The paper provides a simplified proof of convergence for Bézier polynomial approximations on D-dimensional simplices, yielding an error estimate comparable to exponential approximation. The proof uses the topological Stone-Weierstrass theorem.
By using a general formalism, we expose a simplified proof of the convergence of the Bézier polynomials attached to a continuous function defined in arbitrary dimensional simplex. We obtain an error estimate that contains the error in approximating by exponential functions. Our new proof is based on the topological Stone-Weierstrass theorem.