Convergence Rates of AFEM with H1 Data Academic Article

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 2 . The main contribution is to build algorithms that hold for a general right-hand side fH -1 (). Prior work assumes almost exclusively that fL 2 (). New data indicators based on local H -1 norms are introduced, and then the AFEMs are based on a standard bulk chasing strategy (or Drfler 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

authors

• Devore, Ronald

published proceedings

• Foundations of Computational Mathematics

author list (cited authors)

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

citation count

• 26

complete list of authors

• Cohen, Albert||DeVore, Ronald||Nochetto, Ricardo H

publication date

• October 2012

publisher

• Springer Nature  Publisher

published in

• Foundations of Computational Mathematics  Journal

keywords

• 46 Information And Computing Sciences
• 49 Mathematical Sciences
• 4901 Applied Mathematics

Digital Object Identifier (DOI)

• 10.1007/s10208-012-9120-1

start page

• 671

end page

• 718

volume

• 12

issue

• 5