Unified construction and \(L^2\) analysis for the finite volume element method over tensorial meshes
The authors provide the construction and analysis for a family of high order FVE (Finite Volume Element) schemes with the optimal \(L^2\) convergence rate over tensorial meshes in any \(d\)-dimension with \(d\geq 2\). This family includes for instance the existing Gaussian point-based schemes. At the same time, different dual strategies could be allowed in different directions, and the dual strategies could also be asymmetric within each primary tensorial element. This makes it possible to apply FVE scheme to some complex problems. The definition of the tensorial orthogonal condition (TOC) over tensorial meshes in \(d\)-dimension is proposed and analyzed. It is proved that that all the FVE schemes derived from the TOC hold the optimal \(L^2\) convergence rate. Some numerical tests are presented to support the theoretical results.
scientific article; zbMATH DE number 7643020
scientific article