Interior Penalty Procedures for Elliptic and Parabolic Galerkin Methods

Standard Galerkin methods based on C0-piecewise-polynomial spaces often can lead to unsatisfactory approximations of solutions of problems having dominant transport terms. A penalty on the jump in the normal derivative across the interior edges of elements can produce an apparent stiffness intermediate between C0 and C1, and such a method is proposed and analyzed for elliptic and parabolic equations.