scholarly journals Computable a posteriori error estimates in the finite element method based on its local conservativity: improvements using local minimization

2008 ◽  
Vol 24 ◽  
pp. 77-96 ◽  
Author(s):  
Ibrahim Cheddadi ◽  
Radek Fučík ◽  
Mariana I. Prieto ◽  
Martin Vohralík
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimates ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
A Posteriori ◽  
The Finite Element Method ◽  
A Posteriori Error ◽  
Element Method

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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