TY - JOUR
T1 - New Superconvergent Structures with Optional Superconvergent Points for the Finite Volume Element Method
AU - Wang , Xiang
AU - Zhang , Yuqing
AU - Zhang , Zhimin
JO - Communications in Computational Physics
VL - 5
SP - 1332
EP - 1356
PY - 2023
DA - 2023/06
SN - 33
DO - http://doi.org/10.4208/cicp.OA-2022-0295
UR - https://global-sci.org/intro/article_detail/cicp/21763.html
KW - Superconvergence, finite volume, orthogonality condition, tensorial mesh, rectangular mesh.
AB - <p style="text-align: justify;">New superconvergent structures are proposed and analyzed for the finite
volume element (FVE) method over tensorial meshes in general dimension $d$ (for $d≥2$);
we call these orthogonal superconvergent structures. In this framework, one has the freedom to choose the superconvergent points of tensorial $k$-order FVE schemes (for $k≥3$).
This flexibility contrasts with the superconvergent points (such as Gauss points and
Lobatto points) for current FE schemes and FVE schemes, which are fixed. The orthogonality condition and the modified M-decomposition (MMD) technique that are
developed over tensorial meshes help in the construction of proper superclose functions for the FVE solutions and in ensuring the new superconvergence properties of the
FVE schemes. Numerical experiments are provided to validate our theoretical results.</p>