一维奇异非稳态问题全离散解的误差估计

Error Estimates for a Complete Discretization Solution of Singular Time dependent Problem in One Dimension Space

研究如下奇异非稳态问题ｕｔ（ｘ，ｔ）－ｐ－１（ｘ）（ｐ（ｘ）ｕ′（ｘ，ｔ））′＋ｑ（ｘ）ｕ（ｘ，ｔ）＝Ｈ（ｘ，ｔ）ｔ＞０ｘ∈Ｉ≡（０，１）ｕ′（０，ｔ）＝ｕ（１，ｔ）＝０ｔ＞０ｕ（ｘ，０）＝φ（ｘ）｛的有限元方法．分别使用Ｅｕｌｅｒ－Ｇａｌｅｒｋｉｎ方法和Ｃｒａｎｋ－Ｎｉｃｏｌｓｏｎ－Ｇａｌｅｒｋｉｎ方法。

Finite element method is applied to singular time dependent problem in one dimension spaceu t(x,t)-p -1 (x)(p(x)u′(x,t))′+q(x)u(x,t)=H(x,t) t>0 x∈I≡(0,1) u′(0,t)=u(1,t)=0 t>0 u(x,0)=φ(x) Error estimates of a complete descretization solution in weighted L 2 norm are given by Euler Galerkin methods and Crank Nicolson Galerkin methods.