An asymptotic preserving method for linear systems of balance laws based   on Galerkin's method
  We apply the concept of Asymptotic Preserving (AP) schemes to the linearized p-system and discretize the resulting elliptic equation using standard continuous Finite Elements instead of Finite Differences. The fully discrete method is analyzed with respect to consistency, and we compare it numerically with more traditional methods such as Implicit Euler's method. Numerical results indicate that the AP method is indeed superior to more traditional methods. 
Jochen Sch\"utz
math.NA