Event Detail

Event Type: 
Applied Mathematics and Computation Seminar
Monday, March 3, 2014 - 04:00
WNGR 285

Speaker Info

Los Alamos National Laboratory

We present recent developments in the the extension of Finite Elements to
general polygonal meshes. For ease of comparison, we first present a
side-by-side construction of Mimetic Finite Difference (MFD) and Finite
Elements (FE)  discretizations, in the simple example of the Laplace
equation on quadrilateral meshes. Next, we demonstrate how this construction
changes for more general meshes and for other Partial Differential Equations
(PDEs). In particular, we show that the MFD construction is non-unique and
produces a family of discretizations with equivalent properties (e.g.
convergence, stencil size). The MFD family can be presented in a
parameterized form. The number of parameters increases rapidly with the
space dimension, the number of vertices in the polygonal element and the
order of the discretization.The analysis of the family has demonstrated that
the parametric nature of the family can be successfully used to optimize the
discretization for a selected criteria. The most dramatic result is obtained
for wave phenomena on structured meshes, where it is possible to reduce the
numerical dispersion by several orders on structured meshes.
Other examples include enforcement of the discrete maximum principle and the
improvement of convergence for iterative solvers.