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Hybrid Difference Methods for PDEs

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Abstract

We propose the hybrid difference methods for partial differential equations (PDEs). The hybrid difference method is composed of two types of approximations: one is the finite difference approximation of PDEs within cells (cell FD) and the other is the interface finite difference (interface FD) on edges of cells. The interface finite difference is obtained from continuity of some physical quantities. The main advantages of this new approach are that the method can applied to non-uniform grids, retaining the optimal order of convergence and stability of the numerical method for the Stokes equations is obtained without introducing staggered grids.

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Authors and Affiliations

  1. Department of Mathematics, Ajou University, Suwon, 305-701, Korea

    Youngmok Jeon

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  1. Youngmok Jeon
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Correspondence to Youngmok Jeon.

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This author was supported by NRF 2010-0021683.

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Jeon, Y. Hybrid Difference Methods for PDEs. J Sci Comput 64, 508–521 (2015). https://doi.org/10.1007/s10915-014-9941-y

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  • DOI: https://doi.org/10.1007/s10915-014-9941-y

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