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Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. (English) Zbl 0957.65098
The main results of this large paper are as follows. First, the authors develop a tool in order to measure the dispersion for one-, two-, and three dimensional methods. Then, they analyse the classical the \(p\)-version of the Galerkin finite element method (FEM) and some modified methods for square elements. Eventually, they find the best topology against dispersion, for computation with triangular elements.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
Software:
2Dhp90
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References:
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