TY - JOUR
T1 - Analysis of a discontinuous galerkin method for heterogeneous diffusion problems with low-regularity solutions
AU - Di Pietro, Daniele A.
AU - Ern, Alexandre
PY - 2012/7/1
Y1 - 2012/7/1
N2 - We study the convergence of the Symmetric Weighted Interior Penalty discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions only belonging to W 2, p with p ε (1,2]. In 2d, we infer an optimal algebraic convergence rate. In any space dimension d, we achieve the same result for p > 2 d/(d + 2). We also prove convergence without algebraic rates for exact solutions only belonging to the energy space.
AB - We study the convergence of the Symmetric Weighted Interior Penalty discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions only belonging to W 2, p with p ε (1,2]. In 2d, we infer an optimal algebraic convergence rate. In any space dimension d, we achieve the same result for p > 2 d/(d + 2). We also prove convergence without algebraic rates for exact solutions only belonging to the energy space.
KW - discontinuous Galerkin
KW - error analysis
KW - heterogeneous diffusion
UR - https://www.scopus.com/pages/publications/80054725553
U2 - 10.1002/num.20675
DO - 10.1002/num.20675
M3 - Article
AN - SCOPUS:80054725553
SN - 0749-159X
VL - 28
SP - 1161
EP - 1177
JO - Numerical Methods for Partial Differential Equations
JF - Numerical Methods for Partial Differential Equations
IS - 4
ER -