A PRIORI ERROR ESTIMATES OF A DISCONTINUOUS GALERKIN METHOD FOR LINEAR SOBOLEV EQUATIONS∗

ABSTRACT. A discontinuous Galerkin method with interior penalty terms is presented for lin-ear Sobolev equation. On appropriate finite element spaces, we apply a symmetric interior penalty Galerkin method to formulate semidiscrete approximate solutions. To deal with a damp-ing term ∇ · (∇ut) included in Sobolev equations, which is the distinct character compared to parabolic differential equations, we choose special test functions. A priori error estimate for the semidiscrete time scheme is analyzed and an optimal L∞(L2) error estimation is derived 1