New superconvergent structures are introduced by the finite volume element method (FVEM), which allow us to choose the superconvergent points freely. The general orthogonal condition and the modified M-decomposition (MMD) technique are established to prove the superconvergence properties of the new structures. In addition, the relationships between the orthogonal condition and the convergence properties for the FVE schemes are carried out in Table 1. Numerical results are given to illustrate the theoretical results.
Superconvergence of immersed finite volume methods for one-dimensional interface problems
Sun Yat-Sen University（中山大学）；Mississippi State University（密西西比州立大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；Wayne State University（韦恩州立大学）
On a superconvergent lattice Boltzmann boundary scheme
Paris Sud University（巴黎南大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；University El Manar（埃勒曼纳尔大学）；Conservatoire National des Arts et Métiers（国立工艺学院）
A High-Order Finite Volume GENO Scheme with Implicit Time Integration for Three-Temperature Radiation Diffusion Equations
Hong Kong University of Science and Technology（香港科技大学）；Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；National Key laboratory of Computational physics（计算物理国家重点实验室）；Center for Applied Physics and Technology（应用物理与技术中心）；Peking University（北京大学）；Shenzhen Research Institute, Hong Kong University of Science and Technology（香港科技大学深圳研究院）
$O(N)$ Iterative and $O(NlogN)$ Fast Direct Volume Integral Equation Solvers with a Minimal-Rank ${\cal H}^2$-Representation for Large-Scale $3$-D Electrodynamic Analysis
School of Electrical and Computer Engineering, Purdue University（普渡大学电气与计算机工程学院）
An open-source finite volume toolbox for solid mechanics and fluid-solid interaction simulations
University College Dublin（都柏林大学）；University of Zenica（泽尼察大学）；NV Bekaert SA（Bekaert公司）；University of Zagreb（萨格勒布大学）；Johannes Kepler University（约翰内斯·开普勒大学）
Finite volume element method for Landau-Lifshitz equation
Soochow University（苏州大学）；University of Science and Technology of China（中国科学技术大学）；Suzhou Institute for Advanced Research, University of Science and Technology of China（中国科学技术大学苏州高等研究院）
