Summary.
This paper is concerned with the convergence analysis of the local defect correction (LDC) method for diffusion equations. We derive a general expression for the iteration matrix of the method. We consider the model problem of Poisson's equation on the unit square and use standard five-point finite difference discretizations on uniform grids. It is shown via both an upper bound for the norm of the iteration matrix and numerical experiments, that the rate of convergence of the LDC method is proportional to H 2 with H the grid size of the global coarse grid.
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Mathematics Subject Classification (2000): 65N22, 65N50
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Anthonissen, M., Mattheij, R. & Boonkkamp, J. Convergence analysis of the local defect correction method for diffusion equations. Numer. Math. 95, 401–425 (2003). https://doi.org/10.1007/s00211-002-0451-8
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DOI: https://doi.org/10.1007/s00211-002-0451-8