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Journal of Scientific Computing

, Volume 24, Issue 2, pp 163–182 | Cite as

Stabilized Moving Finite Elements for Convection Dominated Problems

  • Keith Miller
Article

Abstract

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.

Keywords

Finite elements moving nodes moving finite elements stabilized finite elements partial differential equations convection advection 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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