Publications (3)0.42 Total impact
Article: Schemes of the finite element method with separation of singularity for a two-point boundary-value problem of the 4th order with degenerate coefficients[show abstract] [hide abstract]
ABSTRACT: In this paper we construct a high accuracy variant of the finite element method for an ordinary differential equation of the fourth order whose coefficients are degenerate on the boundary. The proposed technique is based on the multiplicative and additive-multiplicative separation of singularity. We prove that the convergence rate of the proposed technique is optimal in a given class of smoothness of right-hand sides. Keywords and phrasestwo-point boundary value problem–finite element schemes–weight function spaces–multiplicative and additive-multiplicative separation of singularityRussian Mathematics 05/2012; 55(5):74-77.
Article: High-accuracy schemes of the finite element method for systems of degenerate elliptic equations on an interval[show abstract] [hide abstract]
ABSTRACT: In this paper for the finite elementmethod for systems of degenerate elliptic equations we develop high-accuracy schemes based on multiplicative singularity extraction. We prove theorems about the smoothness of a solution. Based on these theorems we estimate the error of the proposed method.Russian Mathematics 04/2012; 53(7):17-27.
Differential Equations 06/2000; 36(7):1050-1057. · 0.42 Impact Factor