A new expanded mixed method for parabolic integro-differential equations

作者：Liu, Yang^*; Fang, Zhichao; Li, Hong; He, Siriguleng; Gao, Wei

来源：Applied Mathematics and Computation, 2015, 259: 600-613.

DOI：10.1016/j.amc.2015.02.081

• New expanded mixed method
• Parabolic integro-differential equations
• New expanded mixed projection
• Backward Euler scheme
• Error estimates

A new expanded mixed scheme is studied and analyzed for linear parabolic integro-differential equations. The proposed method's gradient belongs to the simple square integrable space replacing the classical H(div;Omega) space. The new expanded mixed projection is introduced, the existence and uniqueness of solution for semi-discrete scheme are proved and the fully discrete error estimates based on both backward Euler scheme are obtained. Moreover, the optimal a priori error estimates in L-2 and H-1-norm for the scalar unknown u and the error results in L-2 (Omega)-norm for its gradient lambda, and its flux sigma (the coefficients times the negative gradient) are derived. Finally, some numerical results are calculated to verify our theoretical analysis.

• 出版日期2015-5-15
• 单位内蒙古大学