Numerical Solution Of The Poisson Equation Over Hypercubes Using Reduced Chebyshev Polynomial Bases

We describe how to use new reduced size polynomial approximations for the numerical solution of the Poisson equation over hypercubes. Our method is based on a non-standard Galerkin method which allows tests functions which do not verify the boundary conditions. Numerical examples are given in dimensions up to 8 on solutions with di erent smoothness using the same approximation basis for both situations. A special attention is paid on conditioning problems. Key words: Reduced size polynomial approximation, Poisson equation on hypercubes, Hybrid variational formulation 1991 MSC: 65C05, 65D15, 65D32, 65N35