Abstract
We derive a priori error estimates in the finite element method for nonselfadjoint elliptic and parabolic interface problems in a two-dimensional convex polygonal domain. Optimal H 1-norm and sub-optimal L 2-norm error estimates are obtained for elliptic interface problems. For parabolic interface problems, the continuous-time Galerkin method is analyzed and an optimal order error estimate in the L 2(0,T;H 1)-norm is established. Further, a discrete-in-time discontinuous Galerkin method is discussed and a related optimal error estimate is obtained. Keywords: Elliptic and parabolic interface problems, finite element method, spatially discrete scheme, discontinuous Galerkin method, error estimates Mathematics Subject Classification (1991): 65N15, 65N20
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