Conservation Properties for the Continuous and Discontinuous Galerkin Methods
نویسندگان
چکیده
In this paper we investigate the relationship between the continuous and the discontinuous Galerkin methods for elliptic problems. In particular, we show that the continuous Galerkin method can be interpreted as the limit of a discontinuous Galerkin method when a stabilization parameter tends to innnity. Based on this observation we derive a method for computing a conservative approximation of the ux on the the boundary of each element for the continuous Galerkin method. The conservative ux is then obtained by actually computing the limit of the natural conservative ux provided by the discontinuous Galerkin method. We prove existence, uniqueness, and optimal order error estimates. Finally, we illustrate our results by a few numerical examples.
منابع مشابه
Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension
Simplified forms of the space-time discontinuous Galerkin (DG) and discontinuous Galerkin least-squares (DGLS) finite element method are developed and analyzed. The new formulations exploit simplifying properties of entropy endowed conservation law systems while retaining the favorable energy properties associated with symmetric variable formulations.
متن کاملMass conservation of the unified continuous and discontinuous element-based Galerkin methods on dynamically adaptive grids with application to atmospheric simulations
We perform a comparison of mass conservation properties of the continuous (CG) and discontinuous (DG) Galerkin methods on non-conforming, dynamically adaptive meshes for two atmospheric test cases. The two methods are implemented in a unified way which allows for a direct comparison of the non-conforming edge treatment. We outline the implementation details of the non-conforming direct stiffnes...
متن کاملOn the Comparison of Evolution Galerkin and Discontinuous Galerkin Schemes
The aim of this paper is to compare some recent numerical schemes for solving hyperbolic conservation laws. We consider the flux vector splitting finite volume methods, finite volume evolution Galerkin scheme as well as the discontinuous Galerkin scheme. All schemes are constructed using time explicit discretization. We present results of numerical experiments for the shallow water equations fo...
متن کاملMultisymplecticity of hybridizable discontinuous Galerkin methods
In this paper, we prove necessary and sufficient conditions for a hybridizable discontinuous Galerkin (HDG) method to satisfy a multisymplectic conservation law, when applied to a canonical Hamiltonian system of partial differential equations. We show that these conditions are satisfied by the “hybridized” versions of several of the most commonly-used finite element methods, including mixed, no...
متن کاملConservative, discontinuous Galerkin-methods for the generalized Korteweg-de Vries equation
Abstract. We construct, analyze and numerically validate a class of conservative, discontinuous Galerkin schemes for the Generalized Korteweg-de Vries equation. Up to round-off error, these schemes preserve discrete versions of the first two invariants (the integral of the solution, usually identified with the mass, and the L–norm) of the continuous solution. Numerical evidence is provided indi...
متن کامل