
Finite element approximation of Lyapunov equations for the computation of quadratic functionals of SPDEs
The computation of quadratic functionals of the solution to a linear sto...
read it

Hilbert–Schmidt regularity of symmetric integral operators on bounded domains with applications to SPDE approximations
Regularity estimates for an integral operator with a symmetric continuou...
read it

Weak convergence of fully discrete finite element approximations of semilinear hyperbolic SPDE with additive noise
We consider the numerical approximation of the mild solution to a semili...
read it

On the Convergence of Numerical Integration as a Finite Matrix Approximation to Multiplication Operator
We study the convergence of a family of numerical integration methods wh...
read it

Inverses of Matern Covariances on Grids
We conduct a theoretical and numerical study of the aliased spectral den...
read it

A probabilistic approach for exact solutions of determinist PDE's as well as their finite element approximations
A probabilistic approach is developed for the exact solution u to a dete...
read it

New Algorithms And Fast Implementations To Approximate Stochastic Processes
We present new algorithms and fast implementations to find efficient app...
read it
Approximation of SPDE covariance operators by finite elements: A semigroup approach
The problem of approximating the covariance operator of the mild solution to a linear stochastic partial differential equation is considered. An integral equation involving the semigroup of the mild solution is derived and a general error decomposition formula is proven. This formula is applied to approximations of the covariance operator of a stochastic advectiondiffusion equation and a stochastic wave equation, both on bounded domains. The approximations are based on finite element discretizations in space and rational approximations of the exponential function in time. Convergence rates are derived in the trace class and Hilbert–Schmidt norms with numerical simulations illustrating the results.
READ FULL TEXT
Comments
There are no comments yet.