A polynomial chaos approach to stochastic variational inequalities
نویسندگان
چکیده
We consider stochastic elliptic variational inequalities of the second kind involving a bilinear form with stochastic diffusion coefficient. We prove existence and uniqueness of weak solutions, propose a stochastic Galerkin approximation of an equivalent parametric reformulation, and show equivalence to a related collocation method. Numerical experiments illustrate the efficiency of our approach and suggest similar error estimates as for linear elliptic problems. AMS classification: 65K15, 65N30, 65N35
منابع مشابه
Variational multiscale stabilized FEM formulations for transport equations: stochastic advection-diffusion and incompressible stochastic Navier-Stokes equations
An extension of the deterministic variational multiscale (VMS) approach with algebraic subgrid scale (SGS) modeling is considered for developing stabilized finite element formulations for the stochastic advection and the incompressible stochastic Navier-Stokes equations. The stabilized formulations are numerically implemented using the spectral stochastic formulation of the finite element metho...
متن کاملSymmetric Confidence Regions and Confidence Intervals for Normal Map Formulations of Stochastic Variational Inequalities
Stochastic variational inequalities (SVI) model a large class of equilibrium problems subject to data uncertainty, and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample average approximation (SAA) problem. This paper considers the normal map formulation of an SVI, and proposes a method to build asymptotically exact confidenc...
متن کاملA probabilistic approach to second order variational inequalities with bilateral constraints
We study a class of second order nonlinear variational inequalities with bilateral constraints. This type of inequalities arises in zero sum stochastic differential games of mixed type where each player uses both continuous control and stopping times. Under a nondegeneracy assumption Bensoussan and Friedman [1,4] have studied this type of problems. They proved the existence of a unique solution...
متن کاملIndividual confidence intervals for true solutions to stochastic variational inequalities
Stochastic variational inequalities (SVI) provide a means for modeling various optimization and equilibrium problems where data are subject to uncertainty. Often it is necessary to estimate the true SVI solution by the solution of a sample average approximation (SAA) problem. This paper proposes three methods for building confidence intervals for components of the true solution, and those inter...
متن کاملA stochastic variational multiscale method for diffusion in heterogeneous random media
A stochastic variational multiscale method with explicit subgrid modeling is provided for solution of stochastic elliptic equations that arise while modeling diffusion in heterogeneous random media [1]. The exact solution of the governing equations is split into two components: a coarse-scale solution and a subgrid solution. A localized computational model for the subgrid solution is derived. T...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Num. Math.
دوره 18 شماره
صفحات -
تاریخ انتشار 2010