Super-Convergence of Autonomous Things

2019 ◽  
Author(s):  
Mohammad Fairus Khalid ◽  
Buhary Ikhwan Ismail ◽  
Rajendar Kandan ◽  
Hong Hoe Ong
Keyword(s):  
Super Convergence

Integro spline quasi-interpolants and their super convergence

2020 ◽  
Vol 39 (3) ◽  
Author(s):  
Jinming Wu ◽  
Wurong Ge ◽  
Xiaolei Zhang
Keyword(s):  
Super Convergence

Numerical Method with the Third-Order ENO Reconstruction Satisfying Two Conversation Laws for Linear Advection Equation

2011 ◽  
Vol 130-134 ◽  
pp. 2969-2972
Author(s):  
Rong San Chen ◽  
An Ping Liu
Keyword(s):  
Numerical Solutions ◽  
Advection Equation ◽  
Finite Volume Schemes ◽  
Third Order ◽  
The Third ◽  
Linear Advection Equation ◽  
Long Time ◽  
Super Convergence ◽  
Better Than ◽  
Eno Scheme

In recent years, Mao and his co-workers developed a class of finite-volume schemes for evolution partial differential equations, see [1-5].The schemes show a super-convergence quality and have good structure-preserving property in long-time numerical simulations. In [6], Chen and Ma developed a scheme which combine the idea of paper [5] and that of the the second-order ENO scheme [7]. In this paper, we propose a scheme which extend the result of [6] and obtain the scheme using the third-order ENO reconstruction. Numerical experiments show that our scheme is robust in long-time behaviors. Numerical solutions are far better than those of [6].

A SMOOTHED FEM (S-FEM) FOR HEAT TRANSFER PROBLEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 1340001 ◽  
Author(s):  
B. Y. XUE ◽  
S. C. WU ◽  
W. H. ZHANG ◽  
G. R. LIU
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Three Dimensions ◽  
Mesh Free ◽  
Theoretical Investigations ◽  
Mesh Free Methods ◽  
Standard Finite Element Method ◽  
Gradient Smoothing ◽  
Transfer Problems ◽  
Super Convergence

By smoothing, via various ways, the compatible strain fields of the standard finite element method (FEM) using the gradient smoothing technique, a family of smoothed FEMs (S-FEMs) has been developed recently. The S-FEM possesses the advantages of both mesh-free methods and the standard FEM and works well with triangular and tetrahedral background cells and elements. Intensive theoretical investigations have shown that the S-FEM models can achieve numerical solutions for many important properties, such as the upper bound solution in strain energy, free from volumetric locking, insensitive to the distortion of the background cells, super-accuracy and super-convergence in displacement or stress solutions or both. Engineering problems, including complex heat transfer problems, have also been analyzed with better accuracy and efficiency. This paper presents the general formulation of the S-FEM for thermal problems in one, two and three dimensions. To examine our formulation, some computational results are compared with those obtained using other established means.

New Energy-Conserved Identitiesand Super-Convergence of the Symmetric Ec-S-Fdtd Scheme for Maxwell’s Equations in 2D

2012 ◽  
Vol 11 (5) ◽  
pp. 1673-1696 ◽  
Author(s):  
Liping Gao ◽  
Dong Liang
Keyword(s):  
Electric Fields ◽  
Maxwell’S Equations ◽  
Numerical Experiments ◽  
Maxwell's Equations ◽  
New Energy ◽  
Efficient Scheme ◽  
Second Order Convergence ◽  
The Magnetic Field ◽  
Super Convergence ◽  
Theoretical Results

AbstractThe symmetric energy-conserved splitting FDTD scheme developed in is a very new and efficient scheme for computing the Maxwell’s equations. It is based on splitting the whole Maxwell’s equations and matching the x-direction and y-direction electric fields associated to the magnetic field symmetrically. In this paper, we make further study on the scheme for the 2D Maxwell’s equations with the PEC boundary condition. Two new energy-conserved identities of the symmetric EC-S-FDTD scheme in the discrete H1-norm are derived. It is then proved that the scheme is uncondi-tionally stable in the discrete H1-norm. By the new energy-conserved identities, the super-convergence of the symmetric EC-S-FDTD scheme is further proved that it is of second order convergence in both time and space steps in the discrete H1-norm. Numerical experiments are carried out and confirm our theoretical results.

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