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- Giving to Math

Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Monday, March 3, 2014 - 04:00

Location:

WNGR 285

Event Link:

Guest Speaker:

Institution:

Los Alamos National Laboratory

Abstract:

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.

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