On the stability of the boundary trace of the polynomial L2L2-projection on triangles and tetrahedra

For the reference triangle or tetrahedron TT, we study the stability properties of the L2(T)L2(T)-projection ΠNΠN onto the space of polynomials of degree NN. We show ‖ΠNu‖L2(∂T)2≤C‖u‖L2(T)‖u‖H1(T). This implies optimal convergence rates for the approximation error ‖u−ΠNu‖L2(∂T)‖u−ΠNu‖L2(∂T) for all u∈Hk(T)u∈Hk(T), k>1/2k>1/2.