矩形域内二阶椭圆型方程奇异摄动问题的边界层格式
The Boundary Layer Scheme for a Singularly Perturbed Problem for the Second Order Elliptic Equation in the Rectangle
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摘要: 利用奇异摄动理论对矩形域内二阶椭圆型奇异摄动方程的Dirichlet问题建立了边界层格式,并作出了误差估计。Abstract: Using singularly perturbation theory is constructed the boundary layer scheme for a Dirichlet problem for the second order singularly perturbed equation of elliptic type in the rectangle. The error estimate is given.
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[1] 苏煜城,《奇异摄动中的边界层校正法》,上海科技出版社(1983). [2] Emelyanov, K.V., A differenee scheme for the equation εΔu+aux1=ƒ, Difference Methods for the Solution of Boundary Problems and Discontinous Boundary Data, ed.G.I, Shishkin, Sverdlovsk(1976), 19-37. [3] Emelyanov, K.V., On a difference scheme for a differential equation with a small parameter affecting the highest derivative, Num.Meth.Mech.Cont.Media, 1, 5(1970). [4] Miller, J.J.H., Construction of an FEM for a Singularly Perturbed Problem in Two Dimensions, ISNM'31, Birkhäuser Verlag, Basel(1976), 165-169. [5] Hsio, G.C.and K.E.Jordan, Solution to the Difference Equations of Singular Perturbation Problem in NASPP, P.W.Hemker and J.J.H.Miller, eds., Academic Press, London(1979), 433-440. [6] Butuzov, V.F., On asymptotic of solutions of singularly perturbed equations of elliptic type in the rectangle, Differential Equations, 11, 6(1975). -
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