Local error analysis of the interior penalty discontinuous Galerkin method for second order elliptic problems

2002 ◽  
Vol 10 (4) ◽  
Author(s):  
G. Kanschat ◽  
R. Rannacher
Keyword(s):  
Error Analysis ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Elliptic Problems ◽  
Second Order ◽  
Local Error ◽  
Interior Penalty ◽  
Second Order Elliptic Problems

scholarly journals An Optimal Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems

2019 ◽  
Vol 19 (4) ◽  
pp. 849-861 ◽  
Author(s):  
Xiao Zhang ◽  
Xiaoping Xie ◽  
Shiquan Zhang
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Convergence Rates ◽  
Elliptic Problems ◽  
Second Order ◽  
Lagrangian Multiplier ◽  
Piecewise Polynomials ◽  
Numer Anal ◽  
Second Order Elliptic Problems

AbstractThe embedded discontinuous Galerkin (EDG) method by Cockburn, Gopalakrishnan and Lazarov [B. Cockburn, J. Gopalakrishnan and R. Lazarov, Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second-order elliptic problems, SIAM J. Numer. Anal. 47 2009, 2, 1319–1365] is obtained from the hybridizable discontinuous Galerkin method by changing the space of the Lagrangian multiplier from discontinuous functions to continuous ones, and adopts piecewise polynomials of equal degrees on simplex meshes for all variables. In this paper, we analyze a new EDG method for second-order elliptic problems on polygonal/polyhedral meshes. By using piecewise polynomials of degrees {k+1}, {k+1}, k ({k\geq 0}) to approximate the potential, numerical trace and flux, respectively, the new method is shown to yield optimal convergence rates for both the potential and flux approximations. Numerical experiments are provided to confirm the theoretical results.

Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems

2020 ◽  
Vol 28 (3) ◽  
pp. 161-174
Author(s):  
Maurice S. Fabien ◽  
Matthew G. Knepley ◽  
Beatrice M. Riviere
Keyword(s):  
Error Estimates ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Computational Cost ◽  
Elliptic Problems ◽  
Second Order ◽  
Three Dimensions ◽  
Galerkin Methods ◽  
Interior Penalty ◽  
Second Order Elliptic Problems

AbstractThe focus of this paper is the analysis of families of hybridizable interior penalty discontinuous Galerkin methods for second order elliptic problems. We derive a priori error estimates in the energy norm that are optimal with respect to the mesh size. Suboptimal L2-norm error estimates are proven. These results are valid in two and three dimensions. Numerical results support our theoretical findings, and we illustrate the computational cost of the method.

scholarly journals A hybridizable direct discontinuous Galerkin method for elliptic problems

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Huiqiang Yue ◽  
Jian Cheng ◽  
Tiegang Liu ◽  
Vladimir Shaydurov
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Elliptic Problems
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