ON COMMUTING p-VERSION PROJECTION-BASED INTERPOLATION ON TETRAHEDRA

摘要

On the reference tetrahedron (K) over cap, we define three projection-based interpolation operators on H-2((K) over cap), H-1((K) over cap, curl), and H-1((K) over cap, div). These operators are projections onto spaces of polynomials, they have the commuting diagram property, and they feature the optimal convergence rate as the polynomial degree increases in H1-s((K) over cap), (H) over tilde (-s)((K) over cap, curl), and (H) over tilde (-s)((K) over cap, div) for 0 <= s <= 1.