Localized direct boundary-domain integro-differential formulations for scalar nonlinear boundary-value problems with variable coefficients
Localized direct boundary-domain integro-differential formulations for scalar nonlinear boundary-value problems with variable coefficients
复制标题
变系数标量非线性边值问题的局部直接边界域积分微分公式
DOI：
10.1007/s10665-004-6089-z
复制
发表时间：
2005
影响因子：
1.3
通讯作者：
S. Mikhailov
中科院分区：
文献类型：
--
作者：
S. Mikhailov
摘要：考虑二阶拟线性椭圆偏微分方程的混合边值问题（BVP），该方程的变系数取决于未知解及其梯度。辅助线性偏微分方程的局部参数以及原始方程和辅助方程的格林恒等式的不同组合用于将 BVP 简化为直接或双算子直接准线性局部边界域积分微分方程 (LBDIDE)。讨论了不同的参数矩阵定位，并提出了相应的非线性 LBDIDE。描述了用于 LBDIDE 离散化的基于网格和无网格的算法，将 LBDIDE 简化为准线性代数方程的稀疏系统。
Abstract.Mixed boundary-value Problems (BVPs) for a second-order quasi-linear elliptic partial differential equation with variable coefficients dependent on the unknown solution and its gradient are considered. Localized parametrices of auxiliary linear partial differential equations along with different combinations of the Green identities for the original and auxiliary equations are used to reduce the BVPs to direct or two-operator direct quasi-linear localized boundary-domain integro-differential equations (LBDIDEs). Different parametrix localizations are discussed, and the corresponding nonlinear LBDIDEs are presented. Mesh-based and mesh-less algorithms for the LBDIDE discretization are described that reduce the LBDIDEs to sparse systems of quasi-linear algebraic equations.