A NEW CHARACTERISTIC EXPANDED MIXED METHOD FOR SOBOLEV EQUATION WITH CONVECTION TERM  

作　　者：YANG LIU HONG LI SIRIGULENG HE ZHICHAO FANG JINFENG WANG 

机构地区：[1]School of Mathematical Sciences Inner Mongolia University Hohhot 010021,China [2]School of Statistics and Mathematics Inner Mongolia University of Finance and Economics Hohhot 010070,China

出　　处：《International Journal of Modeling, Simulation, and Scientific Computing》2014年第1期48-67,共20页建模、仿真和科学计算国际期刊（英文）

基　　金：supported by the National Natural Science Fund of China(11061021);the Scientific Research Projection of Higher Schools of Inner Mongolia(NJZZ12011,NJZY13199);the Natural Science Fund of Inner Mongolia Province(2012MS0108,2012MS0106);the Program of Higher-level talents of Inner Mongolia University(125119,30105-125132).

摘　　要：In this paper,a new numerical method based on a new expanded mixed scheme and the characteristic method is developed and discussed for Sobolev equation with convection term.The hyperbolic part d(x)∂u/∂t+c(x,t)·∇u is handled by the characteristic method and the diffusion term∇·(a(x,t)∇u+b(x,t)∇ut)is approximated by the new expanded mixed method,whose gradient belongs to the simple square integrable(L^(2)(Ω))^(2)space instead of the classical H(div;Ω)space.For a priori error estimates,some important lemmas based on the new expanded mixed projection are introduced.An optimal priori error estimates in L^(2)-norm for the scalar unknown u and a priori error estimates in(L^(2))^(2)-norm for its gradientλ,and its fluxσ(the coefficients times the negative gradient)are derived.In particular,an optimal priori error estimate in H1-norm for the scalar unknown u is obtained.

关 键 词：Sobolev equation new expanded mixed scheme square integrable(L^(2)(Ω))^(2)space characteristic method a priori error estimates 

分 类 号：O17[理学—数学]