Higher-Order Adaptive Finite Difference Methods for Fully Nonlinear Elliptic Equations
Higher-Order Adaptive Finite Difference Methods for Fully Nonlinear Elliptic Equations
复制标题
DOI：
10.1007/s10915-017-0586-5
复制
发表时间：
2018-06-01
影响因子：
2.5
通讯作者：
Salvador, Tiago
中科院分区：
文献类型：
--
作者：
Hamfeldt, Brittany Froese;Salvador, Tiago
介绍了求解全非线性椭圆型偏微分方程的广义有限差分方法。方法基于分段笛卡尔网格，并沿边界增加了附加点。这允许自适应网格和复杂的几何形状，同时仍然确保一致性，单调性和收敛性。本文描述了一种有效计算非传统有限差分模板的算法。我们还提出了一种计算正式高阶收敛方法的策略。算例验证了该方法的有效性、准确性和灵活性。
We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for adaptive meshes and complicated geometries, while still ensuring consistency, monotonicity, and convergence. We describe an algorithm for efficiently computing the non-traditional finite difference stencils. We also present a strategy for computing formally higher-order convergent methods. Computational examples demonstrate the efficiency, accuracy, and flexibility of the methods.