A mixed nonoverlapping covolume method on quadrilateral grids for elliptic problems

• Xiukun Zhao ^[1] ; Yanli Chen ^[3] ; Junliang Lv ^[2]
  1. [1] Eindhoven University of Technology

     Eindhoven University of Technology

     Países Bajos

     
  2. [2] Jilin University

     Jilin University

     China

     
  3. [3] Northeastern University, China

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• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 292, Nº 1 (15 January 2016), 2016, págs. 23-40
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.06.025
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• Resumen

  • A covolume method is proposed for the mixed formulation of second-order elliptic problems. The solution domain is divided by a quadrilateral grid, corresponding to which a nonoverlapping dual grid is constructed. The velocity and pressure are approximated by the lowest-order Raviart–Thomas space on quadrilaterals. We prove its first order optimal rate of convergence for the approximate velocities in the H(div)-norm as well as for the approximate pressures in the L2-norm. A second order error estimate between a suitable projection of the exact velocity (or pressure) and the approximate velocity (or approximate pressure) is also presented. Numerical experiments are provided to illustrate the error behavior of the scheme.