A Two-Level Method for Mimetic Finite Difference Discretizations of\n Elliptic Problems

2013/10/10 by Paola F. Antonietti, Antonietti, Paola F., Marco Verani +3
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1310.2828

openalex publication_date 2013/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose and analyze a two-level method for mimetic finite difference\napproximations of second order elliptic boundary value problems. We prove that\nthe two-level algorithm is uniformly convergent, i.e., the number of iterations\nneeded to achieve convergence is uniformly bounded independently of the\ncharacteristic size of the underling partition. We also show that the resulting\nscheme provides a uniform preconditioner with respect to the number of degrees\nof freedom. Numerical results that validate the theory are also presented.\n

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