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.

scholarly journals Error analysis of the p-version discontinuous Galerkin method for heat transfer in built-up structures

2007 ◽  
Vol 6 (3) ◽  
pp. 719-740
Author(s):  
Kim S. Bey ◽  
◽  
Peter Z. Daffer ◽  
Hideaki Kaneko ◽  
Puntip Toghaw ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Error Analysis ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method

scholarly journals Stability of a Leap-Frog Discontinuous Galerkin Method for Time-Domain Maxwell's Equations in Anisotropic Materials

2017 ◽  
Vol 21 (5) ◽  
pp. 1350-1375 ◽  
Author(s):  
Adérito Araújo ◽  
Sílvia Barbeiro ◽  
Maryam Khaksar Ghalati
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Mesh Size ◽  
Element Space ◽  
First Order ◽  
Balance Accuracy ◽  
The Stability

AbstractIn this work we discuss the numerical discretization of the time-dependent Maxwell's equations using a fully explicit leap-frog type discontinuous Galerkin method. We present a sufficient condition for the stability and error estimates, for cases of typical boundary conditions, either perfect electric, perfect magnetic or first order Silver-Müller. The bounds of the stability region point out the influence of not only the mesh size but also the dependence on the choice of the numerical flux and the degree of the polynomials used in the construction of the finite element space, making possible to balance accuracy and computational efficiency. In the model we consider heterogeneous anisotropic permittivity tensors which arise naturally in many applications of interest. Numerical results supporting the analysis are provided.

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