High order discontinuous Galerkin methods on surfaces

Code:
10/2014
Title:
High order discontinuous Galerkin methods on surfaces
Date:
Monday 17th February 2014
Author(s):
Antonietti, P.F.; Dedner, A.; Madhavan, P.; Stangalino, S.; Stinner, B.; Verani, M.
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Abstract:
We derive and analyze high order discontinuous Galerkin methods for second-order elliptic problems on implicitely defined surfaces in R^3. This is done by carefully adapting the unified discontinuous Galerkin framework of [D.N. Arnold, F. Brezzi, B. Cockburn, and L.D. Marini, SIAM J. Numer. Anal., 2002] on a triangulated surface approximating the smooth surface. We prove optimal error estimates in both a (mesh dependent) energy and L^2 norms.
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SIAM Journal on Numerical Analysis (SINUM)