Error analysis of staggered finite difference finite volume schemes on unstructured meshes
Provides rigorous error analysis for numerical schemes on unstructured meshes, benefiting computational scientists needing reliable discretizations for complex geometries.
This work derives first-order error estimates for finite difference finite volume schemes on unstructured meshes for 1D elliptic and 2D Stokes problems, improving previous results by extending convergence guarantees to unstructured meshes.
This work combines the consistency in lower-order differential operators with external approximations of functional spaces to obtain error estimates for finite difference finite volume schemes on unstructured non-uniform meshes. This combined approach is first applied to the one-dimensional elliptic boundary value problem on non-uniform meshes, and a first-order convergence rate is obtained, which agrees with the results previously reported. The approach is also applied to the staggered MAC scheme for the two-dimensional incompressible Stokes problem on unstructured meshes. A first-order convergence rate is obtained, which improves over a previously reported result in that it also holds on unstructured meshes. For both problems considered in this work, the convergence rate is one order higher on meshes satisfying special requirements.