Superconvergence of immersed finite volume methods for one-dimensional interface problems (Q1691382)

The authors propose a unified approach to study a class of high order immersed finite volume methods (IFVM) for one-dimensional interface problems. Only the main results are reviewed here. Using generalized Lobatto polynomials as the trial function space and the generalized Gauss points as the control volume, they prove the continuity of the associated bilinear form and establish the optimal convergence rate of the IFV approximation, relative to the \(H^1\)-norm and the \(L^2\)-norm. Some superconvergence properties of the IFVM are derived. Numerical examples are given as illustrations.