Convergence Rates of AFEM with H−1 Data Academic Article uri icon

abstract

  • This paper studies adaptive finite element methods (AFEMs), based on piecewise linear elements and newest vertex bisection, for solving second order elliptic equations with piecewise constant coefficients on a polygonal domain Ω⊂ℝ 2 . The main contribution is to build algorithms that hold for a general right-hand side f∈H -1 (Ω). Prior work assumes almost exclusively that f∈L 2 (Ω). New data indicators based on local H -1 norms are introduced, and then the AFEMs are based on a standard bulk chasing strategy (or Dörfler marking) combined with a procedure that adapts the mesh to reduce these new indicators. An analysis of our AFEM is given which establishes a contraction property and optimal convergence rates N -s with 0

author list (cited authors)

  • Cohen, A., DeVore, R., & Nochetto, R. H.

citation count

  • 19

publication date

  • June 2012