The classical heat conduction equation is derived from the assumption that the temperature increases immediately after heat transfer, but the increase of temperature is a slow process, so the memory-dependent heat con...The classical heat conduction equation is derived from the assumption that the temperature increases immediately after heat transfer, but the increase of temperature is a slow process, so the memory-dependent heat conduction model has been reconstructed. Numerical results show that the solution of the initial boundary value problem of the new model is similar to that of the classical heat conduction equation, but its propagation speed is slower than that of the latter. In addition, the propagation speed of the former is also affected by time delay and kernel function.展开更多
In this paper, a new method, exact element method for constructing finite element, is presented. It can be applied to solve nonpositive definite or positive definite partial differential equation with arbitrary variab...In this paper, a new method, exact element method for constructing finite element, is presented. It can be applied to solve nonpositive definite or positive definite partial differential equation with arbitrary variable coefficient under arbitrary boundary condition. Its convergence is proved and its united formula for solving partial differential equation is given. By the present method, a noncompatible element can be obtained and the compatibility conditions between elements can be treated very easily. Comparing the exact element method with the general finite element method with the same degrees of freedom, the high convergence rate of the high order derivatives of solution can be obtained. Three numerical examples are given at the end of this paper, which indicate all results can converge to exact solution and have higher numerical precision.展开更多
文摘The classical heat conduction equation is derived from the assumption that the temperature increases immediately after heat transfer, but the increase of temperature is a slow process, so the memory-dependent heat conduction model has been reconstructed. Numerical results show that the solution of the initial boundary value problem of the new model is similar to that of the classical heat conduction equation, but its propagation speed is slower than that of the latter. In addition, the propagation speed of the former is also affected by time delay and kernel function.
文摘In this paper, a new method, exact element method for constructing finite element, is presented. It can be applied to solve nonpositive definite or positive definite partial differential equation with arbitrary variable coefficient under arbitrary boundary condition. Its convergence is proved and its united formula for solving partial differential equation is given. By the present method, a noncompatible element can be obtained and the compatibility conditions between elements can be treated very easily. Comparing the exact element method with the general finite element method with the same degrees of freedom, the high convergence rate of the high order derivatives of solution can be obtained. Three numerical examples are given at the end of this paper, which indicate all results can converge to exact solution and have higher numerical precision.
