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Endre SüliFinite element approximation of high-dimensional transport-dominated diffusion problemsHigh-dimensional partial differential equations with nonnegative characteristic form arise in numerous mathematical models in science. In problems of this kind, the computational challenge of beating the exponential growth of complexity as a function of dimension is exacerbated by the fact that the problem may be transport-dominated. We develop the analysis of stabilised sparse finite element methods for such high-dimensional, non-self-adjoint and possibly degenerate partial differential equations.Bibliographical note: Published in: Luis-Miguel Pardo, Allan Pinkus, Endre Süli, Michael Todd (Eds.). Foundations of Computational Mathematics, Santander 2005. Cambridge University Press, 2006. |