Workshop on Computation of Kinetic Transport and Related Problems

## A difference finite element method for 3D parabolic problem

### Speaker

Xinlong Feng（冯新龙） , Xinjiang University

### Time

22 Jun, 14:00 - 14:40

### Abstract

In this work, we propose a novel difference finite element (DFE) method based on the $P_1$-element for the 3D heat equation on a bounded domain $\O=\o\times (0,L_3)$. One of novel ideas of this work is to use the second-order backward difference formula (BDF) combining DFE method to overcome the computational complexity of conventional finite element (FE) method for the high-dimensional parabolic problem. The proposed method deduces a numerical solution of the 3D problem on $\O$ into a combination of numerical solutions of a series of 2D problem on $\o$. Finally, numerical tests are presented to show the second-order $H^1$-convergence results of the proposed DFE method for the 3D heat equation.