The linear hyperbolic equation is of great interest inmany branches of physics and industry.In this paper,we use theweak Galerkinmethod to solve the linear hyperbolic equation.Since the weak Galerkin finite element sp...The linear hyperbolic equation is of great interest inmany branches of physics and industry.In this paper,we use theweak Galerkinmethod to solve the linear hyperbolic equation.Since the weak Galerkin finite element space consists of discontinuous polynomials,the discontinuous feature of the equation can be maintained.The optimal error estimates are proved.Some numerical experiments are provided to verify the efficiency of the method.展开更多
In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the a...In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.展开更多
基金The research of R.Zhangwas supported in part by China Natural National Science Foundation(U1530116,91630201,11471141)by the Program for Cheung Kong Scholars of Ministry of Education of China,Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education,Jilin University,Changchun,130012,P.R.China.
文摘The linear hyperbolic equation is of great interest inmany branches of physics and industry.In this paper,we use theweak Galerkinmethod to solve the linear hyperbolic equation.Since the weak Galerkin finite element space consists of discontinuous polynomials,the discontinuous feature of the equation can be maintained.The optimal error estimates are proved.Some numerical experiments are provided to verify the efficiency of the method.
文摘In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.
