In the present paper we introduce a Virtual Element Method (VEM) for the approximate solution of general linear second order elliptic problems in mixed form, allowing for variable coefficients. We derive a theoretical convergence analysis of the method and develop a set of numerical tests on a benchmark problem with known solution.
DOI : 10.1051/m2an/2015067
Mots clés : Mixed Virtual Element Methods, elliptic problems
@article{M2AN_2016__50_3_727_0, author = {Beir\~ao da Veiga, Louren\c{c}o and Brezzi, Franco and Marini, Luisa Donatella and Russo, Alessandro}, title = {Mixed virtual element methods for general second order elliptic problems on polygonal meshes}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {727--747}, publisher = {EDP-Sciences}, volume = {50}, number = {3}, year = {2016}, doi = {10.1051/m2an/2015067}, mrnumber = {3507271}, zbl = {1343.65134}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2015067/} }
TY - JOUR AU - Beirão da Veiga, Lourenço AU - Brezzi, Franco AU - Marini, Luisa Donatella AU - Russo, Alessandro TI - Mixed virtual element methods for general second order elliptic problems on polygonal meshes JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 727 EP - 747 VL - 50 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015067/ DO - 10.1051/m2an/2015067 LA - en ID - M2AN_2016__50_3_727_0 ER -
%0 Journal Article %A Beirão da Veiga, Lourenço %A Brezzi, Franco %A Marini, Luisa Donatella %A Russo, Alessandro %T Mixed virtual element methods for general second order elliptic problems on polygonal meshes %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 727-747 %V 50 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015067/ %R 10.1051/m2an/2015067 %G en %F M2AN_2016__50_3_727_0
Beirão da Veiga, Lourenço; Brezzi, Franco; Marini, Luisa Donatella; Russo, Alessandro. Mixed virtual element methods for general second order elliptic problems on polygonal meshes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 3, pp. 727-747. doi : 10.1051/m2an/2015067. http://www.numdam.org/articles/10.1051/m2an/2015067/
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