一类椭圆型方程边值问题的边界积分方法

Boundary Integral Method for a Kind of Elliptic Equation Boundary Value Problem

以粘弹性结构动力响应问题中的一类椭圆边值问题为背景，采用变分方法系统分析了椭圆方程边值问题，相应边界变分方程及近似边界变分方程解的存在惟一性．给出了近似解的误差估计，构造了具约束的边界积分方法．从理论上完善了粘弹性结构动力响应问题的边界元方法．文末还给出了数值算例．

A kind of elliptic boundary value problem in the dynamic response of a viscoelastic plate is discussed. By applying the variational method, the existence and uniqueness of the solution for the elliptic boundary value problem, the corresponding boundary variational equation and the approximation boundary variational equation are systematically analyzed.The error estimation of the approximation solution is yielded. The boundary integral method with constraint for boundary value problem is constructed. Finally the numerical experiment is given.