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 http://dl.begellhouse.com/journals/52034eb04b657aea,0a2633174192d2ab,0cff99c31c1251f7.html