No. Functions in RT-spaces are vector-valued functions whose normal components are continuous across element interfaces.

Hi Bishnu,

I guess it depends what you call "RT" space. If, for example, you consider the primal formulation of mixed RTk finite elements, then as Martin indicated you impose an H_div condition on this space which forces some continuity of normal components. Hence, some piecewise constant functions will satisfy these continuity conditions (actually, probably not much), but others will not.

If, on the contrary, you consider the dual formulation of RTk FE, then no continuity conditions are imposed through the edges (the Lagrange multipliers take care of that) and the space to consider is that of all functions that are, in each triangle T, of the form P_k(K) + x P^h_k(K) (where P^h_k is the set of homogeneous polynomials of degree k, or 0). In that case, all piecewise constant functions are in the RTk space.

My impression is that "RTk" is a local property (described above) and that the particular continuity properties, or lack thereof, you impose on the global space depends on the problem/formulation you consider. Hence, the answer to your question depends on the kind of global space constructed using the local RTk forms of the functions.

Thank you Martin and Jerome. You are right.