Convergence of adaptive stochastic collocation with finite elements

Convergence rates for adaptive finite elements

In this article we prove that it is possible to construct, using newestvertex bisection, meshes that equidistribute the error in H-norm, whenever the function to approximate can be decomposed as a sum of a regular part plus a singular part with singularities around a finite number of points. This decomposition is usual in regularity results of Partial Differential Equations (PDE). As a conseque...

Tutorial Orthogonal Collocation on Finite Elements

Stochastic collocation and mixed finite elements for flow in porous media

The aim of this paper is to quantify uncertainty of flow in porous media through stochastic modeling and computation of statistical moments. The governing equations are based on Darcy’s law with stochastic permeability. Starting from a specified covariance relationship, the log permeability is decomposed using a truncated Karhunen-Loève expansion. Mixed finite element approximations are used in...

Adaptive Finite Element Methods with convergence rates

Micromechanically based stochastic finite elements

A stochastic finite element method for analysis of effects of spatial variability of material properties is developed with the help of a micromechanics approach. The method is illustrated by evaluating the first and second moments of the global response of a membrane with microstructure of a spatially random inclusionmatrix composite under a deterministic uniformly distributed load. It is shown...