Aiming at the isoparametric bilinear finite volume element scheme,we initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise by employing the energ...Aiming at the isoparametric bilinear finite volume element scheme,we initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise by employing the energy-embedded method on uniform grids.Furthermore,we prove that the approximate derivatives are convergent of order two.Finally,numerical examples verify the theoretical results.展开更多
In this paper, high-order numerical analysis of finite element method（FEM） is presented for twodimensional multi-term time-fractional diffusion-wave equation（TFDWE）. First of all, a fully-discrete approximate sche...In this paper, high-order numerical analysis of finite element method（FEM） is presented for twodimensional multi-term time-fractional diffusion-wave equation（TFDWE）. First of all, a fully-discrete approximate scheme for multi-term TFDWE is established, which is based on bilinear FEM in spatial direction and Crank-Nicolson approximation in temporal direction, respectively. Then the proposed scheme is proved to be unconditionally stable and convergent. And then, rigorous proofs are given here for superclose properties in H-1-norm and temporal convergence in L-2-norm with order O（h-2＋ τ-（3-α））, where h and τ are the spatial size and time step, respectively. At the same time, theoretical analysis of global superconvergence in H-1-norm is derived by interpolation postprocessing technique. At last, numerical example is provided to demonstrate the theoretical analysis.展开更多
基金supported by NSFC Project(Grant No.11031006,91130002,11171281)the Key Project of Scientific Research Fund of Hunan Provincial Science and Technology Department(Grant No.2011FJ2011)+2 种基金Specialized research Fund for the Doctoral Program of Higher Education(Grant No.20124301110003)Program for Changjiang Scholars and Innovative Research Team in University of China(No.IRT1179)Hunan Provincial Natural Science Foundation of China(Grant No.12JJ3010)。
文摘Aiming at the isoparametric bilinear finite volume element scheme,we initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise by employing the energy-embedded method on uniform grids.Furthermore,we prove that the approximate derivatives are convergent of order two.Finally,numerical examples verify the theoretical results.
基金Supported by the National Natural Science Foundation of China(Nos.11771438,11471296)the Key Scientific Research Projects in Universities of Henan Province(No.19B110013)the Program for Scientific and Technological Innovation Talents in Universities of Henan Province(No.19HASTIT025)
文摘In this paper, high-order numerical analysis of finite element method（FEM） is presented for twodimensional multi-term time-fractional diffusion-wave equation（TFDWE）. First of all, a fully-discrete approximate scheme for multi-term TFDWE is established, which is based on bilinear FEM in spatial direction and Crank-Nicolson approximation in temporal direction, respectively. Then the proposed scheme is proved to be unconditionally stable and convergent. And then, rigorous proofs are given here for superclose properties in H-1-norm and temporal convergence in L-2-norm with order O（h-2＋ τ-（3-α））, where h and τ are the spatial size and time step, respectively. At the same time, theoretical analysis of global superconvergence in H-1-norm is derived by interpolation postprocessing technique. At last, numerical example is provided to demonstrate the theoretical analysis.
