Tareq Hamadneh, J. Merker, Willi Schimmel, Gregor Schuldt
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Simplicial Bernstein form and positivity certificates for solutions obtained in a stationary digital twin by Bernstein Bubnov-Galerkin method
In this article, using the simplicial Bernstein form of polynomials on a simplex, we provide positivity certificates for the approximate solution of a linear elliptic PDE obtained by simplicial Bernstein Bubnov-Galerkin method. Particularly, we show how to obtain a simplicial Bernstein certificate of positivity for the approximate solution, although the discretized system does not satisfy a discrete weak maximum principle.
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