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Title: Continuous Galerkin and Enriched Galerkin Methods with Arbitrary Order Discontinuous Trial Functions for the Elliptic and Parabolic Problems with Jump Conditions
Award ID(s):
1913016
PAR ID:
10166996
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of scientific computing
Volume:
84
ISSN:
1573-7691
Page Range / eLocation ID:
9
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  2. The analyses of interior penalty discontinuous Galerkin methods of any order k for solving elliptic and parabolic problems with Dirac line sources are presented. For the steady state case, we prove convergence of the method by deriving a priori error estimates in the L 2 norm and in weighted energy norms. In addition, we prove almost optimal local error estimates in the energy norm for any approximation order. Further, almost optimal local error estimates in the L 2 norm are obtained for the case of piecewise linear approximations whereas suboptimal error bounds in the L 2 norm are shown for any polynomial degree. For the time-dependent case, convergence of semi-discrete and of backward Euler fully discrete scheme is established by proving error estimates in L 2 in time and in space. Numerical results for the elliptic problem are added to support the theoretical results. 
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