
Multilevel Monte Carlo estimators for elliptic PDEs with Lévytype diffusion coefficient
General elliptic equations with spatially discontinuous diffusion coeffi...
read it

Convergence of adaptive stochastic collocation with finite elements
We consider an elliptic partial differential equation with a random diff...
read it

The SPDE approach for Gaussian random fields with general smoothness
A popular approach for modeling and inference in spatial statistics is t...
read it

Preconditioners for robust optimal control problems under uncertainty
The discretization of robust quadratic optimal control problems under un...
read it

Fast sampling of parameterised Gaussian random fields
Gaussian random fields are popular models for spatially varying uncertai...
read it

Surrogate Approximation of the GradShafranov Free Boundary Problem via Stochastic Collocation on Sparse Grids
In magnetic confinement fusion devices, the equilibrium configuration of...
read it

Spatial statistics and stochastic partial differential equations: a mechanistic viewpoint
The Stochastic Partial Differential Equation (SPDE) approach, now common...
read it
Subordinated Gaussian Random Fields in Elliptic Partial Differential Equations
To model subsurface flow in uncertain heterogeneous fractured media an elliptic equation with a discontinuous stochastic diffusion coefficient  also called random field  may be used. In case of a onedimensional parameter space, Lévy processes allow for jumps and display great flexibility in the distributions used. However, in various situations (e.g. microstructure modeling), a onedimensional parameter space is not sufficient. Classical extensions of Lévy processes on two parameter dimensions suffer from the fact that they do not allow for spatial discontinuities. In this paper a new subordination approach is employed to generate Lévytype discontinuous random fields on a twodimensional spatial parameter domain. Existence and uniqueness of a (pathwise) solution to a general elliptic partial differential equation is proved and an approximation theory for the diffusion coefficient and the corresponding solution provided. Further, numerical examples using a Monte Carlo approach on a Finite Element discretization validate our theoretical results.
READ FULL TEXT
Comments
There are no comments yet.