Hierarchical Basis for the Convection-Diffusion Equation on Unstructured Meshes

Hierarchical Basis for the Convection-Diffusion Equation on Unstructured Meshes

Finite integration method with RBFs for solving time-fractional convection-diffusion equation with variable coefficients

In this paper, a modification of finite integration method (FIM) is combined with the radial basis function (RBF) method to solve a time-fractional convection-diffusion equation with variable coefficients. The FIM transforms partial differential equations into integral equations and this creates some constants of integration. Unlike the usual FIM, the proposed method computes constants of integ...

A finite volume method on general meshes for a degenerate parabolic convection-reaction-diffusion equation

We propose a finite volume method on general meshes for the discretization of a degenerate parabolic convection-reaction-diffusion equation. Equations of this type arise in many contexts, such as the modeling of contaminant transport in porous media. We discretize the diffusion term, which can be anisotropic and heterogeneous, via a hybrid finite volume scheme. We construct a partially upwind s...

Multiresolution Approximate Inverse Preconditioners

We introduce a new preconditioner for elliptic PDE’s on unstructured meshes. Using a wavelet-inspired basis we compress the inverse of the matrix, allowing an effective sparse approximate inverse by solving the sparsity vs. accuracy conflict. The key issue in this compression is to use second-generation wavelets which can be adapted to the unstructured mesh, the true boundary conditions, and ev...

Finite Element Methods for Convection Diffusion Equation

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...