A new approach to the analysis of axisymmetric problems.

This paper builds a new framework to analyse axisymmetric problems through differential forms and exterior calculus. We construct a new weighted L2 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. [ABSTRACT FROM AUTHOR]