The Moving Finite Element method (MFE) when applied to purely hyperbolic problems tends to move its nodes with the flow (often a good thing). But for steady or near steady problems the nodes flow past stationary regions of critical interest and pile up at the outflow. We report on efforts to develop moveable node versions of the “stabilized” finite element methods which have so successfully improved upon Galerkin in the fixed node setting. One method in particular (Galerkin-Δx TLSMFE with a “fix”) yields very promising results on our simple 1-D model problem. Its nodes lock onto and resolve sharp stationary features but also lock onto and move with the moving features of the solution.
Finite elements moving nodes moving finite elements stabilized finite elements partial differential equations convection advection
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