拟线性抛物型积分微分方程动边界的有限元法

Full-discrete Finite Element Methods for Semi-Nonlinear Parabolic Integro-differential Equation with Moving Boundary in Two dimension

本文对一类二维拟线性抛物型积分-微分方程动边界问题的有限元方法进行了研究,给出了全离散有限元格式及最佳L2模和能量模误差估计,在这一过程中首先借助积分变换将拟线性方程线性化,然后利用变量代换和Ritz-Volterra投影处理动边界和时间积分项。

Parabolic integro-differential equations can be widely used in describing the heat transfer problems with memory and some gas diffusion problems.This paper studies finite element approximation to the solutions of such equations.The full-discrete finite element scheme is given and the optimal L2 norm and energy norm convergence results are obtained.Integer transformation is used to linear the equation,then variable substituting and the Ritz-Volterra projection are used to deal with moving boundary and the integral with time.