RT Journal Article ID 0cff99c31c1251f7 A1 Anker, Felix A1 Bayer, Christian A1 Eigel, Martin A1 Neumann, Johannes A1 Schoenmakers, John T1 A FULLY ADAPTIVE INTERPOLATED STOCHASTIC SAMPLING METHOD FOR LINEAR RANDOM PDES JF International Journal for Uncertainty Quantification JO IJUQ YR 2017 FD 2017-08-01 VO 7 IS 3 SP 189 OP 205 K1 random PDE K1 stochastic differential equation K1 Feynman-Kac K1 interpolation K1 finite element K1 a posteriori error estimator K1 adaptive method K1 Euler Maruyama AB A numerical method for the fully adaptive sampling and interpolation of linear PDEs with random data is presented. It is based on the idea that the solution of the PDE with stochastic data can be represented as conditional expectation of a functional of a corresponding stochastic differential equation (SDE). The spatial domain is decomposed by a nonuniform grid and a classical Euler scheme is employed to approximately solve the SDE at grid vertices. Interpolation with a conforming finite element basis is employed to reconstruct a global solution of the problem. An a posteriori error estimator is introduced which provides a measure of the different error contributions. This facilitates the formulation of an adaptive algorithm to control the overall error by either reducing the stochastic error by locally evaluating more samples, or the approximation error by locally refining the underlying mesh. Numerical examples illustrate the performance of the presented novel method. PB Begell House LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,0a2633174192d2ab,0cff99c31c1251f7.html