Moving finite elements in 1-D: a review of the method and the coding experience

Technical Report · Thu Sep 01 04:00:00 EDT 1983

OSTI ID:5333588

Sincovec, R; Aslam, S

We developed the code which can solve a system of nonlinear partial differential equations using the moving finite element (MFE) method. We have demonstrated its capabilities by presenting solutions for Burger's equation, reactive and non-reactive square waves, and as required by the contract, Maxwell's equations. We have certainly realized the elegance in the idea and mathematics involved with the MFE method; we are very apprehensive of using the code. Compared to conventional numerical packages, some of which allow the user almost hands off computing, the MFE code places a large burden on the user. We have not been able to come up with a suitable way for selecting the number nodes to use and how to place them initialy. Choosing the optimum values for constants in the regularization term is pure guess work (or so it seems). This combined with the selection of error tolerances for the ODE integrator, and selecting suitable weights for the PDE's makes one very skeptic of obtaining results within a suitable amount of time and effort. When one guesses the parameters right, the results obtained are indeed remarkable. If all the given work could some how be avoided, we strongly feel that the MFE method would be a very powerful tool.

• Research Organization: Colorado Univ., Colorado Springs (USA). Dept. of Computer Science
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 5333588
• Report Number(s): UCRL-15572; ON: DE84004821
• Country of Publication: United States
• Language: English

Related Subjects

658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BURGERS VECTOR
COMPUTER CALCULATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE ELEMENT METHOD
NUMERICAL SOLUTION