Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Moving finite elements
A Geometrical-Mechanical Interpretation of Gradient-Weighted Moving Finite Elements
SIAM Journal on Numerical Analysis
Design and Application of a Gradient-Weighted Moving Finite Element Code I: in One Dimension
SIAM Journal on Scientific Computing
Design and Application of a Gradient-Weighted Moving Finite Element Code II: in Two Dimensions
SIAM Journal on Scientific Computing
Nonlinear Krylov and moving nodes in the method of lines
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
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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-驴x 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.