scholarly journals Sharp maximum norm error estimates for general mixed finite element approximations to second order elliptic equations

1989 ◽  
Vol 23 (1) ◽  
pp. 103-128 ◽  
Author(s):  
Lucia Gastaldi ◽  
Ricardo H. Nochetto
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Elliptic Equations ◽  
Mixed Finite Element ◽  
Second Order ◽  
Maximum Norm ◽  
Sharp Maximum ◽  
Finite Element Approximations ◽  
Second Order Elliptic Equations ◽  
Norm Error

Error Estimates and Iterative Procedure for Mixed Finite Element Solution of Second-Order Quasi-Linear Elliptic Problems

2004 ◽  
Vol 4 (4) ◽  
pp. 445-463 ◽  
Author(s):  
Mikhail Karchevsky ◽  
Alexander Fedotov
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Elliptic Equations ◽  
Iterative Procedure ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Second Order ◽  
Discrete Problem ◽  
Arbitrary Power ◽  
Power Rate

AbstractThe mixed finite element method for second-order quasi-linear elliptic equations with nonlinearities of arbitrary power rate of growth is considered. Error estimates are obtained. An iterative method for corresponding discrete problem is proposed and investigated.

Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations

2016 ◽  
Vol 8 (6) ◽  
pp. 1050-1071 ◽  
Author(s):  
Tianliang Hou ◽  
Li Li
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Elliptic Equations ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Control Variable ◽  
The State ◽  
Control Problems ◽  
General Elliptic

AbstractIn this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L2 and H–1-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

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