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An adaptive stabilized method for advection-diffusion-reaction equation. (English) Zbl 1436.65170

Summary: We introduce and analyze a Residual Local Projection (RELP) adaptive finite element scheme for the advection-reaction-diffusion equation. This scheme is based on L. P. Franca et al. [C. R., Math., Acad. Sci. Paris 347, No. 17–18, 1105–1110 (2009; Zbl 1171.76026)] and combined with a residual a posteriori error estimator (see [R. Verfürth, Numer. Math. 80, No. 4, 641–663 (1998; Zbl 0913.65095)]). The a posteriori estimator is proved to be consistent, reliable, and efficient. More specifically, we proved global upper and local lower error estimates with constants, which are independent of the physical parameters and the mesh-size. Several numerical experiments illustrate the effectiveness of this method.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs

Software:

p1afem; Triangle; TetGen; na14
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Full Text: DOI

References:

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