Higher‐order finite volume element methods based on Barlow points for one‐dimensional elliptic and parabolic problems

The article is devoted to a kind of higher‐order finite volume element methods, where the dual partitions are constructed by Barlow points, for elliptic and parabolic problems in one space dimension. Techniques to derive the stability and to control the nonsymmetry are presented. Superconvergence and the optimal order errors in the H¹‐ and L²‐norms are obtained. Numerical results illustrate the theoretical findings. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 977–994, 2015