  In this paper, we present a hybridized discontinuous Galerkin (HDG) method
for Poisson-type problems with sign-changing coefficients. We introduce a
sign-changing stabilization parameter that results in a stable HDG method
independent of domain geometry and the ratio of the negative and positive
coefficients. Since the Poisson-type problem with sign-changing coefficients is
not elliptic, standard techniques with a duality argument to analyze the HDG
method cannot be applied. Hence, we present a novel error analysis exploiting
the stabilized saddle-point problem structure of the HDG method. Numerical
experiments in two dimensions and for varying polynomial degree verify our
theoretical results.
