A new approach of superconvergence analysis for two-dimensional time fractional diffusion equation

作者：Shi, Dongyang^*; Yang, Huaijun

来源：Computers & Mathematics with Applications, 2018, 75(8): 3012-3023.

DOI：10.1016/j.camwa.2018.01.029

• Time-fractional diffusion equation
• Bilinear finite element
• Fully-discrete scheme
• Superclose and superconvergence

In this paper, a new approach of superconvergent estimate of bilinear finite element is established for two-dimensional time-fractional diffusion equation under fully-discrete scheme. The novelty of this approach is the combination technique of the interpolation and Ritz projection as well as the superclose estimate in H-1-norm between them, which avoids the difficulty of constructing a postprocessing operator for Ritz projection operator, and reduces the regularity requirement of the exact solution. At the same time, three numerical examples are carried out to verify the theoretical analysis.

• 出版日期2018-4-15
• 单位郑州大学