Strong and weak error estimates for the solutions of elliptic partial differential equations with random coefficients


Julia Charrier, ENS Cachan

Abstract: In order to compute the law of the solution of elliptic partial
differential equations with random coefficients, a Galerkin finite
elements method or a stochastic collocation method can be used. These two
methods are based on a finite dimensional approximation of the stochastic
coefficients, which can be achieved via a Karhunen-Loève expansion.
This works focuses on the case of a homogeneous log-normal coefficient,
which is a model often used in hydrogeology. It proposes estimates for
both the strong error and the weak error on the solution, resulting from
the approximation of the coefficients. We obtain a weak convergence rate
which is twice the strong convergence rate.