论文信息 - L2 error estimation for DGFEM for elliptic problems with low regularity

L2 error estimation for DGFEM for elliptic problems with low regularity

Abstract This paper presents an error estimate in the L 2 -norm for the discontinuous Galerkin finite element methods (DGFEM) for elliptic problems with low regularity solutions. The Raviart–Thomas interpolation operator is employed to derive the new result, which complements the mesh-dependent energy norm error estimates in Gudi (2010) [2] . Numerical results corroborate the theoretical analysis.

Lin Mu | Xiu Ye | Jiangguo Liu

[1] Xiu Ye,et al. A posterior error estimate for finite volume methods of the second order elliptic problem , 2011 .

[2] Thirupathi Gudi,et al. Some nonstandard error analysis of discontinuous Galerkin methods for elliptic problems , 2010 .

[3] L. R. Scott,et al. The Mathematical Theory of Finite Element Methods , 1994 .

[4] Susanne C. Brenner,et al. A weakly over-penalized symmetric interior penalty method for the biharmonic problem. , 2010 .

[5] Junping Wang,et al. UNIFIED A POSTERIORI ERROR ESTIMATOR FOR FINITE ELEMENT METHODS FOR THE STOKES EQUATIONS , 2010 .

[6] Thirupathi Gudi,et al. A new error analysis for discontinuous finite element methods for linear elliptic problems , 2010, Math. Comput..

[7] Michel Fortin,et al. Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[8] R. Bruce Kellogg,et al. On the poisson equation with intersecting interfaces , 1974 .

[9] Shuyu Sun,et al. A Locally Conservative Finite Element Method Based on Piecewise Constant Enrichment of the Continuous Galerkin Method , 2009, SIAM J. Sci. Comput..

[10] Béatrice Rivière,et al. Discontinuous Galerkin Methods for Second-Order Elliptic PDE with Low-Regularity Solutions , 2011, J. Sci. Comput..

[11] Douglas N. Arnold,et al. Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems , 2001, SIAM J. Numer. Anal..