scholarly journals A finite element approximation for a class of degenerate elliptic equations

1999 ◽  
Vol 69 (229) ◽  
pp. 41-64 ◽  
Author(s):  
Bruno Franchi ◽  
Maria Carla Tesi
Keyword(s):  
Finite Element ◽  
Elliptic Equations ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Degenerate Elliptic Equations ◽  
Degenerate Elliptic

scholarly journals Topological Derivatives for Semilinear Elliptic Equations

2009 ◽  
Vol 19 (2) ◽  
pp. 191-205 ◽  
Author(s):  
Mohamed Iguernane ◽  
Serguei Nazarov ◽  
Jean-Rodolphe Roche ◽  
Jan Sokolowski ◽  
Katarzyna Szulc
Keyword(s):  
Finite Element ◽  
Convergence Rate ◽  
Error Estimates ◽  
Elliptic Equations ◽  
Numerical Experiments ◽  
Finite Element Approximation ◽  
Semilinear Elliptic Equations ◽  
Element Approximation ◽  
Semilinear Elliptic ◽  
Topological Derivatives

Topological Derivatives for Semilinear Elliptic EquationsThe form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in theL∞norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.

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