A discontinuous Galerkin method with Lagrange multipliers to solve vector electromagnetic problems in two dimensions

2012 ◽  
Author(s):  
Ming-Feng Xue ◽  
Jian-Ming Jin
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Lagrange Multipliers ◽  
Two Dimensions ◽  
Electromagnetic Problems

Multiple-Stencil Dispersion Analysis of the Lagrange Multipliers in a Discontinuous Galerkin Method for the Helmholtz Equation

2003 ◽  
Vol 11 (02) ◽  
pp. 239-254 ◽  
Author(s):  
Isaac Harari ◽  
Charbel Farhat ◽  
Ulrich Hetmaniuk
Keyword(s):  
Helmholtz Equation ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Lagrange Multiplier ◽  
Lagrange Multipliers ◽  
Degrees Of Freedom ◽  
Dispersion Analysis ◽  
Dispersion Properties

We analyze the dispersion properties of elements obtained by a discontinuous Galerkin method with Lagrange multipliers. The dispersion analysis of these elements presents a challenge in that the Lagrange multiplier degrees of freedom are directional, and hence an unbounded mesh is made up of more than one repeating pattern. Two approaches to overcome this difficulty are presented. The similarity in the two sets of results offers mutual validation of the two approaches.

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