scholarly journals On the enhancement of low-order mixed finite element methods for the large deformation analysis of diffusion in solids

2016 ◽  
Vol 107 (5) ◽  
pp. 450-450
Author(s):  
Andreas Krischok ◽  
Christian Linder
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Finite Element Methods ◽  
Mixed Finite Element ◽  
Mixed Finite Element Methods ◽  
Deformation Analysis ◽  
Diffusion In Solids ◽  
Large Deformation Analysis ◽  
Low Order

scholarly journals Low-Order Nonconforming Mixed Finite Element Methods for Stationary Incompressible Magnetohydrodynamics Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Dongyang Shi ◽  
Zhiyun Yu
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Mixed Finite Element ◽  
Approximate Solutions ◽  
Mixed Finite Element Methods ◽  
Optimal Error Estimates ◽  
Stationary Incompressible Magnetohydrodynamics ◽  
Friedrichs Inequality ◽  
Incompressible Magnetohydrodynamics ◽  
Low Order

The nonconforming mixed finite element methods (NMFEMs) are introduced and analyzed for the numerical discretization of a nonlinear, fully coupled stationary incompressible magnetohydrodynamics (MHD) problem in 3D. A family of the low-order elements on tetrahedra or hexahedra are chosen to approximate the pressure, the velocity field, and the magnetic field. The existence and uniqueness of the approximate solutions are shown, and the optimal error estimates for the corresponding unknown variables inL2-norm are established, as well as those in a brokenH1-norm for the velocity and the magnetic fields. Furthermore, a new approach is adopted to prove the discrete Poincaré-Friedrichs inequality, which is easier than that of the previous literature.

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