Geodesic
A nonuniform difference scheme with fourth order of accuracy in a domain with smooth boundary
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 2, pp. 99-117 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is devoted to construction and justification of a nonuniform difference scheme with fourth order of accuracy for a two-dimensional boundary-value problem for an elliptic equation of second order in a domain with smooth curvilinear boundary. This scheme is called nonuniform because a stencil of difference operator alternates from node to node. In interior nodes a nine-point and standard five-point stencils are used. The special type of stencil is used near the boundary. The paper contains a description for constructing the scheme and for the proof accuracy. Numerical tests confirm the theoretical conclusions about the fourth order of accuracy for the approximate solution. 
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E. G. Bykova; V. V. Shaidurov. A nonuniform difference scheme with fourth order of accuracy in a domain with smooth boundary. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 1 (1998) no. 2, pp. 99-117. http://geodesic.mathdoc.fr/item/SJVM_1998_1_2_a0/

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