We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the classical Vector Potential formulation. The Vector Potential is treated as a triplet of , approximated by nodal VEM spaces. However this is not done using three classical -conforming nodal Virtual Elements, and instead we use the Stokes Elements introduced originally in the paper Divergence free Virtual Elements for the Stokes problem on polygonal meshes (ESAIM Math. Model. Numer. Anal. 51 (2017), 509–535) for the treatment of incompressible fluids.
DOI: 10.5802/smai-jcm.40
Keywords: Virtual Element Methods, Serendipity, Magnetostatic problems, Vector Potential
@article{SMAI-JCM_2018__4__399_0, author = {Beir\~ao da Veiga, Louren\c{c}o and Brezzi, Franco and Marini, L. Donatella and Russo, Alessandro}, title = {Virtual {Element} approximations of the {Vector} {Potential} {Formulation} of {Magnetostatic} problems}, journal = {The SMAI Journal of computational mathematics}, pages = {399--416}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {4}, year = {2018}, doi = {10.5802/smai-jcm.40}, mrnumber = {3883675}, zbl = {1416.78024}, language = {en}, url = {http://www.numdam.org/articles/10.5802/smai-jcm.40/} }
TY - JOUR AU - Beirão da Veiga, Lourenço AU - Brezzi, Franco AU - Marini, L. Donatella AU - Russo, Alessandro TI - Virtual Element approximations of the Vector Potential Formulation of Magnetostatic problems JO - The SMAI Journal of computational mathematics PY - 2018 SP - 399 EP - 416 VL - 4 PB - Société de Mathématiques Appliquées et Industrielles UR - http://www.numdam.org/articles/10.5802/smai-jcm.40/ DO - 10.5802/smai-jcm.40 LA - en ID - SMAI-JCM_2018__4__399_0 ER -
%0 Journal Article %A Beirão da Veiga, Lourenço %A Brezzi, Franco %A Marini, L. Donatella %A Russo, Alessandro %T Virtual Element approximations of the Vector Potential Formulation of Magnetostatic problems %J The SMAI Journal of computational mathematics %D 2018 %P 399-416 %V 4 %I Société de Mathématiques Appliquées et Industrielles %U http://www.numdam.org/articles/10.5802/smai-jcm.40/ %R 10.5802/smai-jcm.40 %G en %F SMAI-JCM_2018__4__399_0
Beirão da Veiga, Lourenço; Brezzi, Franco; Marini, L. Donatella; Russo, Alessandro. Virtual Element approximations of the Vector Potential Formulation of Magnetostatic problems. The SMAI Journal of computational mathematics, Volume 4 (2018), pp. 399-416. doi : 10.5802/smai-jcm.40. http://www.numdam.org/articles/10.5802/smai-jcm.40/
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