Multigrid method for H (div) in three dimensions

摘要: We are concerned with the design and analysis of a multigrid algorithm for (div; )-elliptic linear variational problems. The discretization is based on )-conforming Raviart-Thomas elements. A thorough examination relevant bilinear form reveals that separate treatment vector fields in kernel divergence operator its complement paramount. exploit representation discrete solenoidal as curls finite element functions so-called Nedelec spaces. It turns out combined nodal multilevel decomposition both spaces provides foundation viable method. Its Gaus-Seidel smoother involves an extra stage where error components tackled. By means elaborate duality techniques we can show asymptotic optimality case uniform refinement. Numerical experiments confirm typical efficiency actually achieved model