The Helmholtz equation is sometimes supplemented by conditions that include the specification of the boundary value of the divergence of the unknown.In this paper, we study the vector Helmholtz problem in domains of b...The Helmholtz equation is sometimes supplemented by conditions that include the specification of the boundary value of the divergence of the unknown.In this paper, we study the vector Helmholtz problem in domains of both C^(1,1)and Lipschitz.We es- tablish a rigorous variational analysis such as equivalence,existence and uniqueness. And we propose finite element approximations based on the uncoupled solutions.Fi- nally we present a convergence analysis and error estimates.展开更多
The discontinuous Galerkin method is used for solving the two-dimensional equilibrium radiation diffusion equation.We construct the weighted interior penalty method based on the geometric average weight.The semi-impli...The discontinuous Galerkin method is used for solving the two-dimensional equilibrium radiation diffusion equation.We construct the weighted interior penalty method based on the geometric average weight.The semi-implicit integration factor method is applied to the nonlinear ordinary differential equations obtained by the discontinuous Galerkin spatial discretization.Numerical results are presented to demonstrate the validity and reliability of using the discontinuous Galerkin method for solving the highly nonlinear radiation diffusion equation.展开更多
文摘The Helmholtz equation is sometimes supplemented by conditions that include the specification of the boundary value of the divergence of the unknown.In this paper, we study the vector Helmholtz problem in domains of both C^(1,1)and Lipschitz.We es- tablish a rigorous variational analysis such as equivalence,existence and uniqueness. And we propose finite element approximations based on the uncoupled solutions.Fi- nally we present a convergence analysis and error estimates.
基金Supported by the National Natural Science Foundation of China(Nos 11171038,11126279)Youth Foundation of Tianyuan Mathematicsthe Brazilian National Council for Scientific and Technological Development(CNPq).
文摘The discontinuous Galerkin method is used for solving the two-dimensional equilibrium radiation diffusion equation.We construct the weighted interior penalty method based on the geometric average weight.The semi-implicit integration factor method is applied to the nonlinear ordinary differential equations obtained by the discontinuous Galerkin spatial discretization.Numerical results are presented to demonstrate the validity and reliability of using the discontinuous Galerkin method for solving the highly nonlinear radiation diffusion equation.
