ABSTRACT
This conclusion presents some closing thoughts on the key concepts discussed in this book. The book describes the construction of finite-difference schemes for elliptic, parabolic, and hyperbolic equations on logically rectangular grids by means of the support-operators method. This method produces FDSs, which are conservative and mimic the main properties of original differential problems. The numerical experiments show that constructed FDSs are second-order accurate on smooth grids, and first-order accurate on rough grids, which confirms their robustness. Approximation of the general equations of motion, which involve operations on tensor objects, such as the divergence of a tensor and the gradient of vectors. The method of support-operators also was applied to construct finite-difference schemes on different types of grids: triangular grids, Voronoi grids, and grids with local refinement. The properties of the discrete operators, which follow from the construction of FDSs by the support-operators method, can be used to prove convergence theorems for linear and non-linear problems.
