Weighted Moving Finite Elements applied to systems of
Partial Differential Equations
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 shallow
water equations.