Anisotropic mesh adaptation for numerical solution of boundary value problems. (English) Zbl 1060.65125

The authors have a great experience of mesh adaptation techniques from the mathematical analysis point of view but also from numerical implementation practice. Here, they obtain a significant improvement of numerical results valid for a wide range of 2D problems of physics and engineering described by partial differential equations discretized on triangular grids. In this way, they combine the anisotropic mesh adaptation algorithm with a new smoothing procedure.
This new approach is really carefully analyzed and its efficiency is illustrated upon several problems: a singular diffusion problem, a Poisson problem with steep gradients and finally on the geometrically challenging industrial problem of an inviscid transonic flow around NACA0012 profile. Beyond these so attractive contents, the presentation is clear and very nice.


65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76H05 Transonic flows
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
76M10 Finite element methods applied to problems in fluid mechanics
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