Moving Finite Elements [Hardcover]

Bringing together a decade's worth of research stimulated by Miller's original idea of moving finite elements, this important book discusses the interrelationship between the techniques and the theories regarding the method of characteristics, Hamilton's equations, the Legendre transformation, and grid equidistribution. Throughout, the important issues are cogently highlighted, cutting-edge research developments are detailed, and areas for future research are discussed. Students, teachers, and researchers in applied mathematics, numerical analysis, engineering, and the computational sciences will want to read this book.

1. The MFE Method of Miller
2. Transformations and Steep Fronts
3. Exact Semi-Discrete MFE Solutions
4. MFE in 1-D: First-order Equations
5. MFE in 1-D: Second-order Equations
6. MFE in Higher Dimensions
7. Results from the MFE Method
8. The Role of the MFE Method
9. Best Fits with Adjustable Nodes
10. MFE and Moving Best Fits
11. Discussion and Conclusion

The author has brought together work published over the last twelve years on the method of moving finite elements (MFE), a method for numerically solving partial differential equations where the grid moves adaptively as part of the solution. --Mathematical Reviews