A new multiscale algorithm is introduced based on the framework of the heterogeneous multiscale method. The mixed finite element method used ensures continuity of the flux within the entire domain. This method is shown to be free of “resonance error” and uses less memory than the mixed multiscale finite element method. To account for the highstochastic dimensionality of the permeability field, ...

We compare a kernel-based collocation method (meshfree approximation method) with a Galerkin finite element method for solving elliptic stochastic partial differential equations driven by Gaussian noise. The kernel-based collocation solution is a linear combination of reproducing kernels obtained from related differential and boundary operators centered at chosen collocation points. Its random ...

Computational modelling has received significant attention in the research community over the past few decades due to its pronounced contribution in better understanding of the nature, as well as in the development of advanced technologies. The modelling of more and more complex transport physical systems helps the community to address important issues, like identification of environmental prob...