Mixed Finite Elements for Spatial Regression with PDE Penalization

Mixed Finite Elements for Spatial Regression with PDE Penalization

We study a class of models at the interface between statistics and numerical analysis. Specifically, we consider nonparametric regression models for the estimation of spatial fields from pointwise and noisy observations, which account for problem-specific prior information, described in terms of a partial differential equation governing the phenomenon under study. The prior information is incor...

MOX–Report No. 20/2013 Mixed Finite Elements for spatial regression with PDE penalization Azzimonti,

Mixed finite elements for elasticity

There have been many efforts, dating back four decades, to develop stablemixed finite elements for the stress-displacement formulation of the plane elasticity system. This requires the development of a compatible pair of finite element spaces, one to discretize the space of symmetric tensors in which the stress field is sought, and one to discretize the space of vector fields in which the displ...

Multiscale mixed finite elements

In this work, we propose a mixed finite element method for solving elliptic multiscale problems based on a localized orthogonal decomposition (LOD) of Raviart– Thomas finite element spaces. It requires to solve local problems in small patches around the elements of a coarse grid. These computations can be perfectly parallelized and are cheap to perform. Using the results of these patch problems...

Mixed Finite Elements for Elliptic Problems with Tensor Coeecients as Cell-centered Finite Diierences Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Cell-centered Finite Differences

We present an expanded mixed nite element approximation of second order elliptic problems containing a tensor coeecient. The mixed method is expanded in the sense that three variables are explicitly approximated, namely, the scalar unknown, the negative of its gradient, and its ux (the tensor coeecient times the negative gradient). The resulting linear system is a saddle point problem. In the c...