Convergence and quasi-optimality of an adaptive finite element method for controlling L2 errors Academic Article

abstract

• In this paper, a contraction property is proved for an adaptive finite element method for controlling the global L2 error on convex polyhedral domains. Furthermore, it is shown that the method converges in L2 with the best possible rate. The method that is analyzed is the standard adaptive method except that, if necessary, additional refinements are made to keep the meshes sufficiently mildly graded. This modification does not compromise the quasi-optimality of the resulting algorithm. 2010 The Author(s).

authors

• Demlow, Alan

published proceedings

• Numerische Mathematik

author list (cited authors)

• Demlow, A., & Stevenson, R.

citation count

• 25

complete list of authors

• Demlow, Alan||Stevenson, Rob

publication date

• February 2011

publisher

• Springer Nature  Publisher

published in

• Numerische Mathematik  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4903 Numerical And Computational Mathematics

Digital Object Identifier (DOI)

• 10.1007/s00211-010-0349-9

start page

• 185

end page

• 218

volume

• 117

issue

• 2

URL

• http://dx.doi.org/10.1007/s00211-010-0349-9