SuperconvergenceIn this article, a singularly perturbed convection–diffusion equation is solved by a linear finite element method on a Shishkin mesh. By means of an analysis exploiting symmetries in the convective term of the bilinear form, a new superconvergence rate, which improves the existing ...
In subject area: Mathematics The one-dimensional (1D) diffusion equation, also termed Fourier's second law or Fick's second law, is a basic parabolic partial differential equation (PDE) that admits traveling wave solutions. From: Traveling Wave Analysis of Partial Differential Equations, 2012 ...
and we study their large time asymptotics. Depending on K', we obtain either linear diffusion waves (i.e. the fundamental solution of the heat equation) or nonlinear diffusion waves (the fundamental solution of the viscous Burgers equation) in asymptotic expansions of solutions as t -> infinity...
The diffusion equation goes with one initial condition u(x,0)=I(x), where I is a prescribed function. One boundary condition is required at each point on the boundary, which in 1D means that u must be known, u x must be known, or some combination of them. ...
It is my understanding that the question is about solving the 1D diffusion equation using the Crank-Nicolson method
Dynamic light scattering and sedimentation velocity measurements were performed on dilute benzene solutions of poly(macromonomer) with poly(methyl methacrylate) (PMMA) as the backbone chain and polystyrene (PS) as branches to obtain the diffusion coefficient D and the sedimentation coefficient s, respect...
First we demonstrate how to discretize and solve the partial differential equation using piecewise linear functions as bases of the finite element space. The resulting solution, however, commonly lies in unnecessarily high dimensional space of an ordinary differential equation (ODE). We use the proper...
Heat Diffusion Equation In subject area: Engineering Mathematically, the heat diffusion equation is a differential equation that requires integration constants in order to have a unique solution. From: Spacecraft Thermal Control, 2012 About this pageSet alert Discover other topics ...
It is a combination of the Eulerian method, in which the equation is solved on a fixed grid in space, and Lagrangian method that utilizes either a deforming grid or a fixed grid in deforming coordinates. The (ELM) combines aspects of both approaches: so as to merge the simplicity of a ...
We think of diffusion as resulting from one of two broad sets of forces: onein which mounting adoptions of a policy alter the benets of adopting for others and another in whichadoptions provide policy relevant information about the benets of adopting. We develop argumentswithin these broad ...