An interior penalty discontinuous Galerkin reduced order model for the variable coefficient advection–diffusion-reaction equation.

In this paper, we construct a reduced order model (ROM) to solve the advection–diffusion-reaction (ADR) equation with variable coefficients. In order to get the desired fidelity solution, we introduce the interior penalty discontinuous Galerkin (IPDG) and implicit–explicit Runge–Kutta (IMEXRK) schemes to construct the full-order model (FOM). The IPDG scheme can achieve higher-order accuracy in spatial discretization. We split the model into the advection-reaction and diffusion terms so as to ensure the stability of the full-discrete scheme. The IMEXRK scheme discrete the advection-reaction term explicitly and the diffusion term implicitly to obtain a higher-order scheme in time discretization. Then, the POD method and Galerkin projection are introduced to construct the ROM. The resulting ROM can maintain the higher-order accuracy of the original IPDG method and greatly reduce the computation cost. Some numerical examples are used to demonstrate the accuracy and effectiveness of the ROM. [ABSTRACT FROM AUTHOR]