This dissertation aims to study finite element methods for two-dimensional stationary second order interface model problems on homogeneous and heterogeneous media, under discretizations non-fitted with …
The finite element method (FEM) is an extremely successful approach to numerically approximating solutions to partial differential equations arising from many real-world scenarios. While the …
We develop a recursive multistage Wiener chaos expansion method (WCE) and a recursive multi-stage stochastic collocation method (SCM) for numerical integration of linear stochastic advection-diffusion-reaction …