A new expanded mixed element method for convection-dominated Sobolev equation.
We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen's expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in L (2)-norm for the scalar unknown u and a priori error estimates in (L (2))(2)-norm for its gradient λ and its flux σ . Moreover, we obtain the optimal a priori error estimates in H (1)-norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method.
School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China.
Jinfeng
J
Wang
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China.
Yang
0000-0001-8218-0196
Y
Liu
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China.
Hong
H
Li
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China.
Zhichao
Z
Fang
D016014:Linear Models; D008962:Models, Theoretical