COLLOQUIUM
3:004:00 p.m., Wednesday (September 26)
MATH 104
Abigail Wacher
Finavera Renewables Inc.
Weighted Moving Finite Elements applied to systems of Partial Differential Equations
Abstract:
Solving problems containing complex structures or moving shocks using standard methods can be computationally expensive. Using an adaptive mesh to `track' moving fronts
and boundaries has been shown to provide cheaper and more accurate computations, making
them a good candidate for solving large scale problems with a wide variety of applications.
In my talk I will introduce an adaptive mesh technique called ``String Gradient Weighted
Moving Finite Elements" and present results to several systems of nonlinear Partial Differential
Equations (PDEs), including a two dimensional model of a chemical reaction, the porous medium
equation, and solutions to the dispersive and nondispersive nonlinear shallow water equations.
Two deficiencies of the original Moving Finite Element method are (1) possible tangling of
the mesh, and (2) absence of a mechanism for global refinement when necessary due to the constant
number of degrees of freedom. Recently I have studied the SGWMFE method including uniform
remeshing in order to continue computing solutions when the meshes become too distorted. I
have also studied the method when implementing global refinement to enable handling of new
physical phenomena of a smaller scale which may appear during the solution process. It is
shown that the errors in time are kept under control when refinement is necessary.
I shall conclude by presenting the results of applying remeshing and refining with SGWMFE
to the dispersive shallow water equations with varying degrees of rotation.
The speaker is a UFA candidate in the Department of Mathematics and will also give the SCAIM Seminar, Tuesday, Sept. 25th at 12:30 p.m. in WMAX 216.
