Modeling, Computation, Nonlinerarity, Randomness and Waves Seminar
A posteriori error estimate and adaptive sparse grid algorithm for PDEs with random coefficients
In this talk, we consider the stochastic collocation nite element method for approximating the solution to an elliptic partial differential equation with a random coecient. We first derive a residual-based a posteriori error estimate that controls the two sources of error, namely the physical and stochastic spaces discretization. The stochastic error estimator is then used to drive an adaptive sparse grid algorithm which aims at circumventing the so-called curse of dimensionality inherent to tensor grids. Several numerical examples are given to illustrate the performance of the adaptive procedure.
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