Stochastic spectral formulations for elliptic problems, Monte Carlo and QuasiMonte

Summary. We describe new stochastic spectral formulations with very good prop-erties in terms of conditioning. These formulations are built by combining Monte Carlo approximations of the Feynman-Kac formula and standard deterministic ap-proximations on basis functions. We give error bounds on the solutions obtained using these formulations in the case of linear approximations. Some numerical tests are made on an anisotropic diffusion equation using a tensor product Tchebychef polynomial basis and one random point schemes quantified or not.