A new positive definite semi-discrete mixed finite element solution for parabolic equations

a new positive definite semi-discrete mixed finite element solution for parabolic equations

in this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. in the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations.  also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. error estimates were also obtaine...

A New Positive Definite Expanded Mixed Finite Element Method for Parabolic Integrodifferential Equations

A new positive definite expanded mixed finite element method is proposed for parabolic partial integrodifferential equations. Compared to expanded mixed scheme, the new expanded mixed element system is symmetric positive definite and both the gradient equation and the flux equation are separated from its scalar unknown equation. The existence and uniqueness for semidiscrete scheme are proved an...

Semi-discrete Finite Element Approximations for Linear Parabolic Integro-di erential Equations with Integrable Kernels

In this paper we consider nite element methods for general parabolic integro-diierential equations with integrable kernels. A new approach is taken, which allows us to derive optimal L p (2 p 1) error estimates and superconvergence. The main advantage of our method is that the semidiscrete nite element approximations for linear equations, with both smooth and integrable kernels, can be treated ...

Solution of Parabolic Equations by Backward Euler-Mixed Finite Element Methods on a Dynamically Changing Mesh

We develop and analyze methods based on combining the lowest-order mixed finite element method with backward Euler time discretization for the solution of diffusion problems on dynamically changing meshes. The methods developed are shown to preserve the optimal rate error estimates that are well known for static meshes. The novel aspect of the scheme is the construction of a linear approximatio...

Finite Element Methods for Parabolic Equations

The initial-boundary value problem for a linear parabolic equation with the Dirichlet boundary condition is solved approximately by applying the finite element discretization in the space dimension and three types of finite-difference discretizations in time: the backward, the Crank-Nicolson and the Calahan discretization. New error bounds are derived.

Error estimates for a mixed finite element discretization of some degenerate parabolic equations