  Tempered fractional Laplacian is the generator of the tempered isotropic
L\'evy process [W.H. Deng, B.Y. Li, W.Y. Tian, and P.W. Zhang, Multiscale
Model. Simul., 16(1), 125-149, 2018]. This paper provides the finite difference
discretization for the two dimensional tempered fractional Laplacian
$(\Delta+\lambda)^{\frac{\beta}{2}}$. Then we use it to solve the tempered
fractional Poisson equation with Dirichlet boundary conditions and derive the
error estimates. Numerical experiments verify the convergence rates and
effectiveness of the schemes.
