Convergence and quasi-optimality of adaptive finite element methods for harmonic forms Academic Article

abstract

• 2017, Springer-Verlag Berlin Heidelberg. Numerical computation of harmonic forms (typically called harmonic fields in three space dimensions) arises in various areas, including computer graphics and computational electromagnetics. The finite element exterior calculus framework also relies extensively on accurate computation of harmonic forms. In this work we study the convergence properties of adaptive finite element methods (AFEM) for computing harmonic forms. We show that a properly defined AFEM is contractive and achieves optimal convergence rate beginning from any initial conforming mesh. This result is contrasted with related AFEM convergence results for elliptic eigenvalue problems, where the initial mesh must be sufficiently fine in order for AFEM to achieve any provable convergence rate.

authors

• Demlow, Alan

published proceedings

• Numerische Mathematik

author list (cited authors)

• Demlow, A.

citation count

• 10

complete list of authors

• Demlow, Alan

publication date

• August 2017

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/s00211-016-0862-6

start page

• 941

end page

• 971

volume

• 136

issue

• 4

URL

• http://dx.doi.org/10.1007/s00211-016-0862-6