A POD-based reduced-order TSCFE extrapolation iterative format for two-dimensional heat equations

作者：Luo Zhendong^*

来源：Boundary Value Problems, 2015, 2015(1): 59.

DOI：10.1186/s13661-015-0320-x

• proper orthogonal decomposition technique
• reduced-order time-space finite element extrapolation iterative format
• two-dimensional heat equations
• error estimate

In this article, a proper orthogonal decomposition (POD) technique is employed to establish a POD-based reduced-order time-space continuous finite element (TSCFE) extrapolation iterative format for two-dimensional (2D) heat equations, which includes very few degrees of freedom but holds sufficiently high accuracy. The error estimates of the POD-based reduced-order TSCFE solutions and the algorithm implementation of the POD-based reduced-order TSCFE extrapolation iterative format are provided. A numerical example is used to illustrate that the results of the numerical computation are consistent with the theoretical conclusions. Moreover, it is shown that the POD-based reduced-order TSCFE extrapolation iterative format is feasible and efficient for solving 2D heat equations.

• 出版日期2015-4-4
• 单位华北电力大学（保定）; 华北电力大学