Stability-enhanced AP IMEX1-LDG Method: Energy-based Stability and Rigorous AP Property

In our recent work [Z. Peng et al., J. Comput. Phys., 415 (2020), 109485], a family of high-order asymptotic preserving (AP) methods, termed IMEX-LDG are designed to solve some linear kinetic transport equations, including the one-group equation in slab geometry and telegraph equation, diffusive scaling. As Knudsen number $\varepsilon$ goes zero, limiting schemes implicit discretizations equation. Both Fourier analysis numerical experiments imply methods unconditionally stable regime when $\varepsilon\ll1$. this paper, we develop an energy approach establish stability IMEX1-LDG method, subfamily that is first-order accurate time arbitrary order space, for model with general material properties. Our first simultaneously confirm unconditional $\varepsilon\ll 1$ uniform property respect $\varepsilon$. To capture stability, propose novel discrete explore various stabilization mechanisms method their relative contributions different regimes. A form weight function, introduced obtain 1$, also considered such analysis. Based on rigorous then carried out show AP property.