一类二维非线性奇异稳态问题的有限元方法

Finite Element Method for a Class of Nonlinear Singular Elliptic Problems in Two Dimensional Space

考虑二维非线性边值问题L u =-〔1xσ x(xσa(x,y,u) u x) + y(a(x,y,u) u y〕 =f (x,y) ,(x,y)∈Ωu|Γ0 =0的有限元方法 ,利用 Banach不动点定理 ,证明了弱解的存在、唯一性 .给出了有限元解的最佳阶的加权 L2 模和加权

We consider the finite element method for two dimensional singular nonlinear boundary value problems.The existence and uniqueness of solution is proved.Optimal error estimates in weighted L 2 norm and weighted H 1 norm are obtained.