
doi: 10.1137/0728070
The author tries, and I think he successfully attempts, to find a deeper understanding of the moving finite element (MFE) method. First he establishes the relationship between MFE and the method of characteristics in the case of a first order partial differential equation and then he brings out the connections between MFE and the Legendre transformation.
Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, adaptive grid methods, finite element method, element-by-element projection, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Legendre transformation, nodal movement, method of characteristics, node-by-node projection
Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs, adaptive grid methods, finite element method, element-by-element projection, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Legendre transformation, nodal movement, method of characteristics, node-by-node projection
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