A POSTERIORI ERROR ANALYSIS FOR CRANK-NICOLSON-GALERKIN TYPE METHODS FOR REACTION-DIFFUSION EQUATIONS WITH DELAY

作者：Wang, Wansheng^*; Rao, Ting; Shen, Weiwei; Zhong, Peng

来源：SIAM Journal on Scientific Computing, 2018, 40(2): A1095-A1120.

DOI：10.1137/17M1143514

• parabolic delay differential equations
• reaction-diffusion equations with delay
• a posteriori error estimates
• Crank-Nicolson-Galerkin method
• Crank-Nicolson method
• delay-dependent reconstruction

We study a posteriori error estimates of Crank-Nicolson-Galerkin type methods for time discretizations of reaction-diffusion equations with delay. In view of the weak discontinuous property of the solutions to delay equations, a posteriori error estimates are of utmost important in numerically solving this class of equations. To derive optimal order a posteriori error estimates, delay-dependent reconstructions for both the Crank-Nicolson-Galerkin method and the Crank-Nicolson method are introduced. By using these continuous, piecewise-quadratic time reconstructions, the upper and lower error bounds depending only on the discretization parameters and the data of the problems are derived. Numerical studies are reported for several test cases, and they verify our theoretical results

• 出版日期2018
• 单位上海师范大学; 长沙理工大学