scholarly journals Two dimensional mixed finite element approximations for elliptic problems with enhanced accuracy for the potential and flux divergence

2017 ◽  
Vol 74 (12) ◽  
pp. 3283-3295 ◽  
Author(s):  
Agnaldo M. Farias ◽  
Philippe R.B. Devloo ◽  
Sônia M. Gomes ◽  
Denise de Siqueira ◽  
Douglas A. Castro
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Elliptic Problems ◽  
Two Dimensional ◽  
Flux Divergence ◽  
Finite Element Approximations

scholarly journals On mixed finite element techniques for elliptic problems

1983 ◽  
Vol 6 (4) ◽  
pp. 755-766 ◽  
Author(s):  
M. Aslam Noor
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Numerical Approximation ◽  
Mixed Finite Element ◽  
Elliptic Problems ◽  
Energy Functional ◽  
Nonlinear Elliptic Problems ◽  
Finite Element Approximations ◽  
Nonlinear Elliptic ◽  
Extended Variational Principle

The main aim of this paper is to consider the numerical approximation of mildly nonlinear elliptic problems by means of finite element methods of mixed type. The technique is based on an extended variational principle, in which the constraint of interelement continuity has been removed at the expense of introducing a Lagrange multiplier.It is shown that the saddle point, which minimizes the energy functional over the product space, is characterized by the variational equations. The eauivalence is used in deriving the error estimates for the finite element approximations. We give an example of a mildly nonlinear elliptic problem and show how the error estimates can be obtained from the general results.

scholarly journals Two dimensional hierarchical mixed finite element approximations with enhanced primal variable accuracy

2017 ◽  
Author(s):  
Agnaldo Farias ◽  
Philippe Devloo ◽  
Sônia Gomes ◽  
Denise De Siqueira ◽  
Douglas Castro
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Two Dimensional ◽  
Finite Element Approximations
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