A Parallel Newton Multigrid Method for High Order Nite Elements and Its Application to Numerical Existence Proofs for Elliptic Boundary Value Equations
نویسنده
چکیده
We describe a parallel algorithm for the numerical computation of guaranteed bounds for solutions of elliptic boundary value equations of second order. We use C 2-Hermite elements and a parallel Newton multigrid method to produce approximations of high accuracy. Then, we compute upper bounds for the defect and enclosures for the eigenvalues of the linearization. In order to obtain veriied bounds, these computations are realized in interval arithmetic. The application of the Newton-Kantorovich-theorem yields the existence of a solution and error bounds for the approximation. The method is implemented on a 256 processor transputer grid and tested for the Bratu problem ?u = exp(u).
منابع مشابه
A Parallel Newton Multigrid Method for High Order Nite Elements and Its Application on Numerical Existence Proofs for Elliptic Boundary Value Equations
We describe a parallel algorithm for the numerical computation of guaranteed bounds for solutions of elliptic boundary value equations of second order. We use C 2-Hermite-elements and a parallel Newton multigrid method to produce approximations of high accuracy. Then, we compute upper bounds for the defect and enclosures for the eigenvalues of the linearization. In order to obtain veriied bound...
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