Detailed Elementary Applications
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This chapter deals with elementary applications of PC methods in idealized settings, specifically involving the heat equation in 2D and the 1D Burgers equation. Attention is focused on the intrusive formalism. Furthermore, we restrict ourselves to steady problems, the extension of the methods to transient situations being relatively straightforward. Within this restricted framework, we strive to provide a detailed outline of the formulation of the stochastic problem, the discretization schemes employed, and solution methods for the resulting discrete stochastic systems.
KeywordsHeat Equation Burger Equation Expansion Order Deterministic Problem Galerkin Projection
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