Discontinuous Galerkin Finite Element Method for the Wave Equation
نویسندگان
چکیده
منابع مشابه
Discontinuous Galerkin Finite Element Method for the Wave Equation
The symmetric interior penalty discontinuous Galerkin finite element method is presented for the numerical discretization of the second-order wave equation. The resulting stiffness matrix is symmetric positive definite and the mass matrix is essentially diagonal; hence, the method is inherently parallel and leads to fully explicit time integration when coupled with an explicit timestepping sche...
متن کاملThe local discontinuous Galerkin finite element method for Burger's equation
In this paper, we study the local discontinuous Galerkin (LDG) finite element method for solving a nonlinear Burger’s equation with Dirichlet boundary conditions. Based on the Hopf–Cole transformation, we transform the original problem into a linear heat equation with Neumann boundary conditions. The heat equation is then solved by the LDG finite element method with special chosen numerical flu...
متن کاملMixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
In this paper, we first split the biharmonic equation !2u = f with nonhomogeneous essential boundary conditions into a system of two second order equations by introducing an auxiliary variable v = !u and then apply an hp-mixed discontinuous Galerkin method to the resulting system. The unknown approximation vh of v can easily be eliminated to reduce the discrete problem to a Schur complement sys...
متن کاملA space-time finite element method for the nonlinear Schröinger equation: the discontinuous Galerkin method
The convergence of the discontinuous Galerkin method for the nonlinear (cubic) Schrödinger equation is analyzed in this paper. We show the existence of the resulting approximations and prove optimal order error estimates in L∞(L2). These estimates are valid under weak restrictions on the space-time mesh.
متن کاملA Space-time Finite Element Method for the Nonlinear Schrödinger Equation: the Discontinuous Galerkin Method
The convergence of the discontinuous Galerkin method for the nonlinear (cubic) Schrödinger equation is analyzed in this paper. We show the existence of the resulting approximations and prove optimal order error estimates in L∞(L2). These estimates are valid under weak restrictions on the space-time mesh.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2006
ISSN: 0036-1429,1095-7170
DOI: 10.1137/05063194x