We investigate a finite element approximation of an initial boundary value problem associated with parabolic Partial Differential Equations endowed with mixed time varying boundary conditions, switching from essential to natural and vice versa. The switching occurs both in time and in different portions of the boundary. For this problem, we apply and extend the Nitsche’s method presented in [Juntunen and Stenberg, Math. Comput. (2009)] to the case of mixed time varying boundary conditions. After proving existence and numerical stability of the full discrete numerical solution obtained by using the -method for time discretization, we present and discuss a numerical test that compares our method to a standard approach based on remeshing and projection procedures.
DOI: 10.1051/m2an/2015054
Keywords: Nitsche’s method, parabolic problems, mixed time varying boundary conditions, stability analysis, finite element method
@article{M2AN_2016__50_2_541_0, author = {Tagliabue, Anna and Ded\`e, Luca and Quarteroni, Alfio}, title = {Nitsche{\textquoteright}s method for parabolic partial differential equations with mixed time varying boundary conditions}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {541--563}, publisher = {EDP-Sciences}, volume = {50}, number = {2}, year = {2016}, doi = {10.1051/m2an/2015054}, mrnumber = {3482554}, zbl = {1382.65327}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2015054/} }
TY - JOUR AU - Tagliabue, Anna AU - Dedè, Luca AU - Quarteroni, Alfio TI - Nitsche’s method for parabolic partial differential equations with mixed time varying boundary conditions JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 541 EP - 563 VL - 50 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015054/ DO - 10.1051/m2an/2015054 LA - en ID - M2AN_2016__50_2_541_0 ER -
%0 Journal Article %A Tagliabue, Anna %A Dedè, Luca %A Quarteroni, Alfio %T Nitsche’s method for parabolic partial differential equations with mixed time varying boundary conditions %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 541-563 %V 50 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015054/ %R 10.1051/m2an/2015054 %G en %F M2AN_2016__50_2_541_0
Tagliabue, Anna; Dedè, Luca; Quarteroni, Alfio. Nitsche’s method for parabolic partial differential equations with mixed time varying boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 50 (2016) no. 2, pp. 541-563. doi : 10.1051/m2an/2015054. http://www.numdam.org/articles/10.1051/m2an/2015054/
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