zbMATH — the first resource for mathematics

A new approach to the analysis of axisymmetric problems. (English) Zbl 1303.65038
Summary: This paper builds a new framework to analyse axisymmetric problems through differential forms and exterior calculus. We construct a new weighted \(L^{2}\) de Rham complex that arises when analysing axi-symmetric problems. By constructing its dual complex, we obtain a Hodge decomposition and a Poincaré inequality in weighted spaces, and the well-posedness of the weighted mixed Hodge Laplacian problem. The stability and convergence of the discrete weighted mixed Hodge Laplacian problem are also achieved by using bounded cochain projections.

65J05 General theory of numerical analysis in abstract spaces
58J05 Elliptic equations on manifolds, general theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
PDF BibTeX Cite
Full Text: DOI