A meteoroid penetrating the Earth's atmosphere leaves behind a trail of dense plasma embedded in the lower E/upper D region ionosphere. While radar measurements of meteor trail evolution have been collected and used to infer meteor and atmospheric properties since the 1950s, no accurate quantitative model of trail fields and diffusion exists. This paper describes finite element simulations of trail plasma physics applicable to the majority of small meteors. Unlike earlier research, our simulations resolve both the trail and a vast current closure area in the background ionosphere. This paper also summarizes a newly developed analytical theory of meteor electrodynamics and shows that our simulations and theory predict nearly identical fields and diffusion rates. This study should enable meteor and atmospheric researchers to more accurately interpret radar observations of specular and nonspecular meteor echoes.