Mathematics

We present some general families of H(div)-conforming and H(curl)‐conforming Virtual Element Spaces on polygonal and polyhedral decompositions. These spaces could be used, together with the more classical $H^1$ conforming Virtual Elements (see [1], [2]) and with the usual discontinuous piecewise polynomial spaces, in order to approximate boundary value problems for Partial Differential Equations in mixed formulation. These spaces generalize the Mixed Virtual Elements of [3], and previous Mimetic Finite Differences for Mixed Formulations. (see e.g. [4]).

REFERENCES
[1] Beirão da Veiga L., Brezzi F., Cangiani A., Manzini G., Marini L.D., Russo A. (2013) Basic Principles of Virtual Element Methods. Math. Models Methods Appl. Sci. 23(1): 199-214.
[2] Ahmed B., Alsaedi A., Brezzi F., Marini L.D., Russo A. (2013) Equivalent Projectors for Virtual Element Methods. Comput. Math. Appl. 66(3): 376-391.
[3] Brezzi F., Falk R.S., Marini L.D (2014) Basic Principles of Mixed Virtual Element Methods. ESAIM Mathematical Models and Numerical Analysis. 48 (4): 1227-1240.
[4] Beirão da Veiga L., Lipnikov K, Manzini G., The Mimetic Finite Difference Method for Elliptic Problems, Springer, MS&A,Vol 11.