Skip to main content
eScholarship
Open Access Publications from the University of California

UC Irvine

UC Irvine Previously Published Works bannerUC Irvine

Decoupling of mixed methods based on generalized Helmholtz decompositions

  • Author(s): Chen, L
  • Huang, X
  • et al.
Abstract

A framework to systematically decouple high order elliptic equations into a combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes and Helmholtz decompositions in a general way. Discretizing the decoupled formulation leads to a natural superconvergence between the Galerkin projection and the decoupled approximation. Examples include but are not limited to the primal formulations and mixed formulations of the biharmonic equation, fourth order curl equation, and triharmonic equation. As a byproduct, Helmholtz decompositions for many dual spaces are obtained.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View