scholarly journals local null controllability for a parabolic equation with local and nonlocal nonlinearities in moving domains

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
André da Rocha Lopes ◽  
Juan Límaco
Keyword(s):  
Parabolic Equation ◽  
Null Controllability ◽  
Moving Domains ◽  
Nonlocal Nonlinearities

Null controllability for a parabolic equation with nonlocal nonlinearities

2012 ◽  
Vol 61 (1) ◽  
pp. 107-111 ◽  
Author(s):  
Enrique Fernández-Cara ◽  
Juan Limaco ◽  
Silvano B. de Menezes
Keyword(s):  
Parabolic Equation ◽  
Null Controllability ◽  
Nonlocal Nonlinearities

scholarly journals Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains

2022 ◽  
Author(s):  
Erik Burman ◽  
Stefan Frei ◽  
Andre Massing
Keyword(s):  
Parabolic Equation ◽  
Stokes Equations ◽  
A Priori ◽  
Time Dependent ◽  
Numerical Examples ◽  
Time Stepping ◽  
Discretisation Error ◽  
Moving Domains ◽  
Theoretical Results ◽  
Norm Error

AbstractThis article is concerned with the discretisation of the Stokes equations on time-dependent domains in an Eulerian coordinate framework. Our work can be seen as an extension of a recent paper by Lehrenfeld and Olshanskii (ESAIM: M2AN 53(2):585–614, 2019), where BDF-type time-stepping schemes are studied for a parabolic equation on moving domains. For space discretisation, a geometrically unfitted finite element discretisation is applied in combination with Nitsche’s method to impose boundary conditions. Physically undefined values of the solution at previous time-steps are extended implicitly by means of so-called ghost penalty stabilisations. We derive a complete a priori error analysis of the discretisation error in space and time, including optimal $$L^2(L^2)$$ L 2 ( L 2 ) -norm error bounds for the velocities. Finally, the theoretical results are substantiated with numerical examples.

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