Weak Galerkin Finite Element Method for Second Order Parabolic Equations
نویسندگان
چکیده
We apply in this paper the weak Galerkin method to the second order parabolic differential equations based on a discrete weak gradient operator. We establish both the continuous time and the discrete time weak Galerkin finite element schemes, which allow using the totally discrete functions in approximation space and the finite element partitions of arbitrary polygons with certain shape regularity. We show as well that the continuous time weak Galerkin finite element method preserves the energy conservation law. The optimal convergence order estimates in both H1 and L2 norms are obtained. Numerical experiments are performed to confirm the theoretical results.
منابع مشابه
Eulerian Finite Element Methods for Parabolic Equations on Moving Surfaces
Three new Eulerian finite element methods for parabolic PDEs on a moving surface Γ(t) are presented and compared in numerical experiments. These are space-time Galerkin methods, which are derived from a weak formulation in space and time. The trialand test-spaces contain the traces on the space-time manifold of an outer prismatic finite element space. The numerical experiments show that two of ...
متن کاملMesh Modification for Evolution Equations
Finite element methods for which the underlying function spaces change with time are studied. The error estimates produced are all in norms that are very naturally associated with the problems. In some cases the Galerkin solution error can be seen to be quasi-optimal. K. Miller's moving finite element method is studied in one space dimension; convergence is proved for the case of smooth solutio...
متن کاملA weak Galerkin finite element method for second-order elliptic problems
In this paper, authors shall introduce a finite element method by using a weakly defined gradient operator over discontinuous functions with heterogeneous properties. The use of weak gradients and their approximations results in a new concept called discrete weak gradients which is expected to play important roles in numerical methods for partial differential equations. This article intends to ...
متن کاملSome Convergence Estimates for Semidiscrete Type Schemes for Time-Dependent Nonselfadjoint Parabolic Equations
Lj-norm error estimates are shown for semidiscrete (continuous in time) Galerkin finite element type approximations to solutions of general time-dependent nonselfadjoint second order parabolic equations under Dirichlet boundary conditions. The semidiscrete solutions are defined in terms of given methods for the corresponding elliptic problem such as the standard Galerkin method in which the bou...
متن کاملA weak Galerkin mixed finite element method for second order elliptic problems
A new weak Galerkin (WG) method is introduced and analyzed for the second order elliptic equation formulated as a system of two first order linear equations. This method, called WG-MFEM, is designed by using discontinuous piecewise polynomials on finite element partitions with arbitrary shape of polygons/polyhedra. The WG-MFEM is capable of providing very accurate numerical approximations for b...
متن کامل