In this paper, a brief review of tailored finite point
methods (TFPM) is given. The TFPM is a new approach to construct the numerical solutions of
partial differential equations. The TFPM has been tailored based on the local properties of the
solution for each given problem.
Especially, the TFPM is very efficient for solutions
which are not smooth enough, e.g., for solutions possessing boundary/interior layers
or solutions being highly oscillated. Recently,
the TFPM has been applied to singular perturbation problems,
the Helmholtz equation with high wave numbers, the first-order wave equation in high frequency cases,
transport equations with interface,
second-order elliptic equations with rough or highly oscillatory coefficients, etc.