Virtual Element Implementation for General Elliptic Equations

2016 ◽  
pp. 39-71 ◽  
Author(s):  
Lourenco Beirão da Veiga ◽  
Franco Brezzi ◽  
Luisa Donatella Marini ◽  
Alessandro Russo
Keyword(s):  
Elliptic Equations ◽  
General Elliptic ◽  
Virtual Element

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.

Fast Factorization Update for General Elliptic Equations Under Multiple Coefficient Updates

2020 ◽  
Vol 42 (2) ◽  
pp. A1174-A1199
Author(s):  
Xiao Liu ◽  
Jianlin Xia ◽  
Maarten de Hoop
Keyword(s):  
Elliptic Equations ◽  
General Elliptic

Superconvergence of Any Order Finite Volume Schemes for 1D General Elliptic Equations

2013 ◽  
Vol 56 (3) ◽  
pp. 566-590 ◽  
Author(s):  
Waixiang Cao ◽  
Zhimin Zhang ◽  
Qingsong Zou
Keyword(s):  
Finite Volume ◽  
Elliptic Equations ◽  
Finite Volume Schemes ◽  
General Elliptic
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