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Moving finite element methods for evolutionary problems. II: Applications. (English) Zbl 0665.65072
[For part I see ibid. 79, No.2, 245-269 (1988; reviewed above).]
Authors’ summary: In this, the second of two papers on the subject, we present applications of the moving finite element method to a number of test problems. Key features are linear elements, a direct approach to parallelism and node overtaking (avoiding penalty functions), rapid inversion of the mass matrix by preconditioned conjugate gradients, and explicit Euler time stepping. The resulting codes are fast and efficient and are able to follow fronts and similar features with great accuracy. The paper includes a substantial section on changes of dependent variable and front tracking techniques for nonlinear diffusion problems. Test problems include non-linear hyperbolic conservation laws and non-linear parabolic equations in one and two dimensions.
Reviewer: R.Gorenflo

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
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