【作者】 菅肖霞；

【导师】 李宏；

【作者基本信息】 内蒙古大学 ， 计算数学， 2008， 硕士

【摘要】 本文将hp-时间间断Galerkin有限元方法应用于拟线性常积分微分方程,然后进一步推广用于偏积分微分方程.首先考虑了拟线性带弱奇异核的Volterra积分微分方程,利用线性化的手段对原问题进行处理,证明了原问题和线性化问题的等价性,最后给出了有限元解的L₂模误差估计.对于拟线性抛物型积分微分方程,同样采用线性化的方法,利用原问题和线性化问题的等价性,证明了在hp-时间间断Galerkin有限元方法下,拟线性抛物型积分微分方程的有限元解的存在唯一性,又对此近似解做出了L₂模误差估计.更多还原

【Abstract】 In this paper the hp-discontinuous Galerkin time-stepping method for quasi-linear ordinary integro-differential equations and then for partial integro-differential equations are considered. Firstly, we consider quasi-linear Volterra integro-differential equations with weakly singular kernels. The primary problems are linearized and the equivalence of the primary problems and the linearized ones are proved. And the error estimates in L₂ are derived. For quasi-linear parabolic integro-differential equations, similarly, using the linearization method and the equivalence of the primary problems and the linearized ones, under the hp-discontinuous Galerkin time-stepping method the existence and uniqueness of the numerical solution of quasi-linear parabolic integro-differential equations are proved. And the error estimates in L₂ are derived.更多还原