Introduction to Gradient-weighted Moving Finite Elements

Keith Miller, University of California, Berkeley
March 4th, 2015 at 2:30PM–3:30PM in 939 Evans Hall [Map]

GWMFE is especially suited to PDE problems with sharp moving fronts. The moving nodes tend to concentrate and move with the fronts, allowing far fewer nodes and much larger timesteps. It does this by treating the solution as an evolving manifold and discretizes with an evolving piecewise linear manifold. I will explain the variational and mechanical interpretations of GWMFE, our BDF2 stiff ODE solver,and our nonlinear Krylov solver for the implicit equations. I will show 2D graphics for the Shallow Water Equations, for Normal and Vertical Motion by Mean Curvature, for the Stefan Problem for melting ice, and also an example from Neil Carlson's 3D GWMFE code. I will discuss the necessity of adding global adaptivity to our codes (insertion and deletion of nodes, flipping edges) and my largely unsuccessful search for "stabilized" versions of MFE which prevent nodes from drifting with the flow in transient advection problems.