A posteriori error estimates with the finite element method of lines for a Sobolev equation

2005 ◽  
Vol 21 (3) ◽  
pp. 521-535 ◽  
Author(s):  
Thanh Tran ◽  
Thanh-Binh Duong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimates ◽  
A Posteriori Error Estimates ◽  
Method Of Lines ◽  
Posteriori Error ◽  
A Posteriori ◽  
The Finite Element Method ◽  
Sobolev Equation ◽  
A Posteriori Error

A POSTERIORI ERROR ESTIMATES FOR THE FOKKER–PLANCK AND FERMI PENCIL BEAM EQUATIONS

2000 ◽  
Vol 10 (05) ◽  
pp. 737-769 ◽  
Author(s):  
MOHAMMAD ASADZADEH
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimates ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Pencil Beam ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Beam Equations ◽  
Element Method

We prove a posteriori error estimates for a finite element method for steady-state, energy dependent, Fokker–Planck and Fermi pencil beam equations in two space dimensions and with a forward-peaked scattering (i.e. with velocities varying within the right unit semi-circle). Our estimates are based on a transversal symmetry assumption, together with a strong stability estimate for an associated dual problem combined with the Galerkin orthogonality of the finite element method.

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