Related Experiment Video
Updated: Dec 11, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
A Posteriori Error Estimates for Fully Discrete Finite Element Method for Generalized Diffusion Equation with Delay
Wansheng Wang1,2, Lijun Yi1, Aiguo Xiao3
1Department of Mathematics, Shanghai Normal University, Shanghai, 200234 China.
Abstract:
In this paper, we derive several a posteriori error estimators for generalized diffusion equation with delay in a convex polygonal domain. The Crank-Nicolson method for time discretization is used and a continuous, piecewise linear finite element space is employed for the space discretization. The a posteriori error estimators corresponding to space discretization are derived by using the interpolation estimates. Two different continuous, piecewise quadratic reconstructions are used to obtain the error due to the time discretization. To estimate the error in the approximation of the delay term, linear approximations of the delay term are used in a crucial way. As a consequence, a posteriori upper and lower error bounds for fully discrete approximation are derived for the first time. In particular, long-time a posteriori error estimates are obtained for stable systems. Numerical experiments are presented which confirm our theoretical results.
More Related Videos
06:55Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
11:34Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels
Published on: September 8, 2016
Related Concept Videos
Poisson's And Laplace's Equation
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Second Order systems II
Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models
Major Losses in Pipes
Fluid flow can be classified as laminar or turbulent, primarily based on the Reynolds number. This dimensionless number reflects the relative influence of inertial to viscous...
Transmission-Line Differential Equations
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...