scholarly journals An optimal-order error estimate for the discontinuous Galerkin method

1988 ◽  
Vol 50 (181) ◽  
pp. 75-75 ◽  
Author(s):  
Gerard R. Richter
Keyword(s):  
Error Estimate ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Optimal Order ◽  
Order Error

scholarly journals A Mixed Discontinuous Galerkin Method for the Helmholtz Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Qingjie Hu ◽  
Yinnian He ◽  
Tingting Li ◽  
Jing Wen
Keyword(s):  
Helmholtz Equation ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Scattered Field ◽  
Numerical Experiments ◽  
Optimal Order ◽  
Flux Variable ◽  
Optimal Order Convergence ◽  
Element Pair

In this paper, we introduce and analyze a mixed discontinuous Galerkin method for the Helmholtz equation. The mixed discontinuous Galerkin method is designed by using a discontinuous Pp+1−1−Pp−1 finite element pair for the flux variable and the scattered field with p≥0. We can get optimal order convergence for the flux variable in both Hdiv-like norm and L2 norm and the scattered field in L2 norm numerically. Moreover, we conduct the numerical experiments on the Helmholtz equation with perturbation and the rectangular waveguide, which also demonstrate the good performance of the mixed discontinuous Galerkin method.

scholarly journals A new mixed discontinuous Galerkin method for the electrostatic field

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Abdelhamid Zaghdani ◽  
Mohamed Ezzat
Keyword(s):  
Error Analysis ◽  
Electric Field ◽  
Error Estimate ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Electrostatic Field ◽  
Mesh Size ◽  
Numerical Results

AbstractWe introduce and analyze a new mixed discontinuous Galerkin method for approximation of an electric field. We carry out its error analysis and prove an error estimate that is optimal in the mesh size. Some numerical results are given to confirm the theoretical convergence.

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