Improved error estimation of dynamic finite element methods for second-order parabolic equations

Dynamic Finite Element Methods for Second Order Parabolic Equations

Dynamic nite element schemes are analyzed for second order parabolic problems. These schemes can employ di erent nite element spaces at di erent time levels in order to capture time-changing localized phenomena, such as moving sharp fronts or layers. The dynamically changing grids and interpolation polynomials are necessary and essential to many large-scale transient problems. Standard, charact...

Weak Galerkin Finite Element Method for Second Order Parabolic Equations

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 regular...

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.

Space-time Finite Element Methods for Second-order Hyperbolic Equations*

Space-time finite element methods are presented to accurately solve elastodynamics problems that include sharp gradients due to propagating waves. The new methodology involves finite element discretization of the time domain as well as the usual finite element discretization of the spatial domain. Linear stabilizing mechanisms are included which do not degrade the accuracy of the space-time fin...

Pointwise localized error estimates for parabolic finite element equations