Analysis of an Embedded Discontinuous Galerkin Method with Implicit-Explicit Time-Marching for Convection-Diffusion Problems

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Abstract

In this paper, we analyze implicit-explicit (IMEX) Runge-Kutta (RK) time discretization methods for solving linear convection-diffusion equations. The diffusion operator is treated implicitly via the embedded discontinuous Galerkin (EDG) method and the convection operator explicitly via the upwinding discontinuous Galerkin method.

Keywords:

Embedded discontinuous Galerkin method upwinding discontinuous Galerkin method implicit-explicit Runge-Kutta time-marching scheme convection-diffusion equation stability error estimate energy method.
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