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A sequential least squares method for Poisson equation using a patch reconstructed space. (English) Zbl 1432.65170

Summary: We propose a new least squares finite element method to solve the Poisson equation. By using a piecewisely irrotational space to approximate the flux, we split the classical method into two sequential steps. The first step gives the approximation of flux in the new approximation space, and the second step can use flexible approaches to give the pressure. The new approximation space for flux is constructed by patch reconstruction with one unknown per element consisting of piecewisely irrotational polynomials. The error estimates in the energy norm and \(L^2\) norm are derived for the flux and the pressure. Numerical results verify the convergence order in error estimates and demonstrate the flexibility and particularly the great efficiency of our method.

MSC:

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

Software:

PolyMesher; Gmsh
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Full Text: DOI arXiv

References:

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