A parallel finite element post-processing algorithm for the damped Stokes equations. (English) Zbl 1538.65555
Summary: This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method and post-processing technique. The most valuable highlights of the present algorithm are that (1) a global continuous approximate solution is generated via the partition of unity method; (2) by adding an extra coarse grid correction step, the smoothness of the approximate solution is improved; (3) it has a good parallel performance since there requires little communication in solving a series of residual problems in the subdomain of interest. We theoretically derive the \(L^2\)-error estimates both for the approximate velocity and pressure and \(H^1\)-error estimate for the velocity under some necessary conditions. Meanwhile, we numerically perform various test examples to validate the theoretically predicted convergence rate and illustrate the high efficiency of the proposed algorithm.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 35Q30 | Navier-Stokes equations |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 65Y05 | Parallel numerical computation |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
Keywords:
partition of unity; Stokes equations; damping; parallel algorithm; two-level method; post-processingReferences:
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