Abstract:
In this paper, we present the totally volume integral of the local discontinuous Galerkin TVLDG method to solve the time-dependent linear convection-diffusion equation, the considered
equation is discretized in space by the local discontinuous Galerkin method after the boundaries integral is transformed into the volume integral by employing the divergence theorem.
The time discretization is accomplished by the third-order strong stability preserving Runge
Kutta explicit SSP-RK (3, 3) method. Numerical solutions are compared with analytical solutions and other methods. The obtained results show that the totally volume integral of the local
discontinuous Galerkin method is one of the most efficient methods for solving the time-dependent linear advection-diffusion equations
