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Higher-order Adaptive Finite Difference Methods for Fully Nonlinear Elliptic Equations. (arXiv:1706.07741v1 [math.NA])
来源于:arXiv
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. 查看全文>>