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Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations. (English) Zbl 1191.65156

The authors are interested to a nonlinear approximation type approach for the solution of high dimensional partial differential equations. This approach is shown on the Poisson equation. A variational version of this approach is analyzed and convergence is shown. Various theoretical and numerical difficulties are shown arising from the non-variational version of the algorithm.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35G50 Systems of nonlinear higher-order PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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References:

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