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L 2 ‐estimates for the DG IIPG‐0 scheme
Author(s) -
de Dios Blanca Ayuso,
Brezzi Franco,
Havle Oto,
Marini L. Donatella
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20687
Subject(s) - mathematics , dimension (graph theory) , order (exchange) , discontinuous galerkin method , scheme (mathematics) , partial derivative , partial differential equation , galerkin method , mathematical analysis , pure mathematics , finite element method , physics , finance , economics , thermodynamics
We discuss the optimality in L 2 of a variant of the Incomplete Discontinuous Galerkin Interior Penalty method (IIPG) for second order linear elliptic problems. We prove optimal estimate, in two and three dimensions, for the lowest order case under suitable regularity assumptions on the data and on the mesh. We also provide numerical evidence, in one dimension, of the necessity of the regularity assumptions. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012