On the stability of the $L_2$ projection in fractional Sobolev spaces

Summary.   In this paper we prove the stability of the projection onto the finite element trial space of piecewise polynomial, in particular, piecewise linear basis functions in for . We formulate explicit and computable local mesh conditions to be satisfied which depend on the Sobolev index s. In conclusion we prove a stability condition needed in the numerical analysis of mixed and hybrid boundary element methods as well as in the construction of efficient preconditioners in adaptive boundary and finite element methods. Received October 14, 1999 / Revised version received March 24, 2000 / Published online October 16, 2000