scholarly journals Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

2016 ◽  
Vol 38 (5) ◽  
pp. A2912-A2933 ◽  
Author(s):  
D. Z. Kalchev ◽  
C. S. Lee ◽  
U. Villa ◽  
Y. Efendiev ◽  
P. S. Vassilevski
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Finite Element Discretization ◽  
Element Discretization

scholarly journals A Finite Element Method for Elliptic Dirichlet Boundary Control Problems

2020 ◽  
Vol 20 (4) ◽  
pp. 827-843
Author(s):  
Michael Karkulik
Keyword(s):  
Finite Element ◽  
Boundary Control ◽  
Dirichlet Boundary ◽  
Mixed Finite Element ◽  
Lagrangian Multiplier ◽  
Finite Element Discretization ◽  
Dirichlet Boundary Control ◽  
Element Discretization ◽  
Polygonal Domains ◽  
Constrained Problems

AbstractWe consider the finite element discretization of an optimal Dirichlet boundary control problem for the Laplacian, where the control is considered in {H^{1/2}(\Gamma)}. To avoid computing the latter norm numerically, we realize it using the {H^{1}(\Omega)} norm of the harmonic extension of the control. We propose a mixed finite element discretization, where the harmonicity of the solution is included by a Lagrangian multiplier. In the case of convex polygonal domains, optimal error estimates in the {H^{1}} and {L_{2}} norm are proven. We also consider and analyze the case of control constrained problems.

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