From formal numerical solutions of elliptic PDE’s to the true ones

Wiener, Z.; Yomdin, Y.

doi:10.1090/S0025-5718-99-01147-3

From formal numerical solutions of elliptic PDE’s to the true ones
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by Z. Wiener and Y. Yomdin PDF

Math. Comp. 69 (2000), 197-235 Request permission

Abstract:

We propose a discretization scheme for a numerical solution of elliptic PDE’s, based on local representation of functions, by their Taylor polynomials (jets). This scheme utilizes jet calculus to provide a very high order of accuracy for a relatively small number of unknowns involved.

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