A super-parallel mixed explicit discontinuous Galerkin method for the second-order Boltzmann-based constitutive models of rarefied and microscale gases

2017 ◽  
Vol 157 ◽  
pp. 146-163 ◽  
Author(s):  
L. Prince Raj ◽  
S. Singh ◽  
A. Karchani ◽  
R.S. Myong
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Constitutive Models ◽  
Second Order

scholarly journals Affine Discontinuous Galerkin Method Approximation of Second-Order Linear Elliptic Equations in Divergence Form with Right-Hand Side in L1

2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Abdeluaab Lidouh ◽  
Rachid Messaoudi
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Divergence Form ◽  
Second Order ◽  
Discrete Problem ◽  
Renormalized Solution ◽  
Order Linear ◽  
Right Hand ◽  
The Right

We consider the standard affine discontinuous Galerkin method approximation of the second-order linear elliptic equation in divergence form with coefficients in L∞Ω and the right-hand side belongs to L1Ω; we extend the results where the case of linear finite elements approximation is considered. We prove that the unique solution of the discrete problem converges in W01,qΩ for every q with 1≤q<d/d-1 (d=2 or d=3) to the unique renormalized solution of the problem. Statements and proofs remain valid in our case, which permits obtaining a weaker result when the right-hand side is a bounded Radon measure and, when the coefficients are smooth, an error estimate in W01,qΩ when the right-hand side f belongs to LrΩ verifying Tkf∈H1Ω for every k>0, for some r>1.

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