Convergence of Finite-Difference Schemes for Elliptic Equations with Variable Coefficients

Open Access

1 July 1987

journal article
Published by Oxford University Press (OUP) in IMA Journal of Numerical Analysis

Vol. 7 (3) , 301-305
https://doi.org/10.1093/imanum/7.3.301

Abstract

We study the convergence of finite-difference schemes for second-order elliptic equations with variable coefficients. We prove that the convergence rate in the discrete W₂¹ norm is of the order h^{s −1} if the solution of the boundary value problem belongs to the Sobolev space W₂^s (1 < s ≤ 3).

Keywords

CONVERGENCE RATE
BOUNDARY VALUE PROBLEM
DIFFERENCE SCHEMES
NORM
ORDER ELLIPTIC
PROBLEM BELONGS
ORDER HS
DISCRETE W21

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