Convergence of a Fully Discrete Scheme for Two-Dimensional Neutron Transport

1983 ◽  
Vol 20 (5) ◽  
pp. 951-966 ◽  
Author(s):  
Claes Johnson ◽  
Juhani Pitkäranta
Keyword(s):  
Neutron Transport ◽  
Two Dimensional ◽  
Discrete Scheme ◽  
Fully Discrete

A numerical method for two-dimensional nonlinear modified time-fractional fourth-order diffusion equation

2019 ◽  
Vol 10 (01) ◽  
pp. 1941005 ◽  
Author(s):  
Haiyan He ◽  
Kaijie Liang ◽  
Baoli Yin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Fourth Order ◽  
Time Derivative ◽  
Second Order ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Discrete Scheme ◽  
Fully Discrete

In this paper, we consider the finite element method for two-dimensional nonlinear modified time-fractional fourth-order diffusion equation. In order to avoid using higher order elements, we introduce an intermediate variable [Formula: see text] and translate the fourth-order derivative of the original problem into a second-order coupled system. We discretize the fractional time derivative terms by using the [Formula: see text]-approximation and discretize the first-order time derivative term by using the second-order backward differentiation formula. In the fully discrete scheme, we implement the finite element method for the spatial approximation. Unconditional stability of the fully discrete scheme is proven and its optimal convergence order is obtained. Numerical experiments are carried out to demonstrate our theoretical analysis.

scholarly journals The Upwind Finite Volume Element Method for Two-Dimensional Burgers Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Qing Yang
Keyword(s):  
Finite Volume ◽  
Burgers Equation ◽  
Volume Element ◽  
Two Dimensional ◽  
Finite Volume Element Method ◽  
Nonlinear Convection ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Finite Volume Element ◽  
Element Method

A finite volume element method for approximating the solution to two-dimensional Burgers equation is presented. Upwind technique is applied to handle the nonlinear convection term. We present the semi-discrete scheme and fully discrete scheme, respectively. We show that the schemes are convergent to order one in space inL2-norm. Numerical experiment is presented finally to validate the theoretical analysis.

scholarly journals Discontinuous finite volume element method of two-dimensional unsaturated soil water movement problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Fan Chen ◽  
Zhixiao Xu
Keyword(s):  
Soil Water ◽  
Finite Volume ◽  
Unsaturated Soil ◽  
Water Movement ◽  
Optimal Error Estimate ◽  
Two Dimensional ◽  
Fully Discrete ◽  
Volume Method ◽  
Movement Problem ◽  
Soil Water Movement

AbstractIn this paper, a numerical approximation method for the two-dimensional unsaturated soil water movement problem is established by using the discontinuous finite volume method. We prove the optimal error estimate for the fully discrete format. Finally, the reliability of the method is verified by numerical experiments. This method is not only simple to calculate, but also stable and reliable.

Semi-Discrete and Fully Discrete Hybrid Stress Finite Element Methods for Elastodynamic Problems

2015 ◽  
Vol 8 (4) ◽  
pp. 582-604
Author(s):  
Zhengqin Yu ◽  
Xiaoping Xie
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Stability Result ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Discrete Scheme ◽  
Fully Discrete ◽  
Quadrilateral Finite Element ◽  
Hybrid Stress Finite Element ◽  
Hybrid Stress

AbstractThis paper proposes and analyzes semi-discrete and fully discrete hybrid stress finite element methods for elastodynamic problems. A hybrid stress quadrilateral finite element approximation is used in the space directions. A second-order center difference is adopted in the time direction for the fully discrete scheme. Error estimates of the two schemes, as well as a stability result for the fully discrete scheme, are derived. Numerical experiments are done to verify the theoretical results.

scholarly journals Numerical Approximation for Fractional Neutron Transport Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhengang Zhao ◽  
Yunying Zheng
Keyword(s):  
Transport Equation ◽  
Nuclear Reactor ◽  
Neutron Transport ◽  
Transport Processes ◽  
Neutron Transport Equation ◽  
Spatial Direction ◽  
Fully Discrete ◽  
Discrete Methods ◽  
Fifth Order ◽  
Different Order

Fractional neutron transport equation reflects the anomalous transport processes in nuclear reactor. In this paper, we will construct the fully discrete methods for this type of fractional equation with Riesz derivative, where the generalized WENO5 scheme is used in spatial direction and Runge–Kutta schemes are adopted in temporal direction. The linear stabilities of the generalized WENO5 schemes with different stages and different order ERK are discussed detailed. Numerical examples show the combinations of forward Euler/two-stage, second-order ERK and WENO5 are unstable and the three-stage, third-order ERK method with generalized WENO5 is stable and can maintain sharp transitions for discontinuous problem, and its convergence reaches fifth order for smooth boundary condition.

Sign in / Sign up

Export Citation Format

Share Document