A Wavelet-Based Adaptive Finite Element Method for Advection-Diffusion Equations

1997 ◽  
Vol 07 (02) ◽  
pp. 265-289 ◽  
Author(s):  
C. Canuto ◽  
I. Cravero
Keyword(s):  
Finite Element ◽  
Unstructured Mesh ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Element Mesh ◽  
Convection Diffusion ◽  
Grid Points ◽  
Convection Dominated ◽  
Steady Convection ◽  
Diffusion Problems

We propose a wavelet-based procedure for adapting a finite element mesh to the structure of the solution. After a finite element solution is computed on a given unstructured mesh, it is wavelet-analyzed on a superimposed regular dyadic grid; the analysis leads to an adapted distribution of grid points, which defines the new unstructured mesh via a Delaunay triangulation. Several examples of discretizations of steady convection-diffusion problems in the convection-dominated regime indicate the feasibility of our approach.

scholarly journals Characteristics Weak Galerkin Finite Element Methods for Convection-Dominated Diffusion Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ailing Zhu ◽  
Qiang Xu ◽  
Ziwen Jiang
Keyword(s):  
Finite Element ◽  
Optimal Order ◽  
Weak Galerkin ◽  
Order Error ◽  
Galerkin Finite Element ◽  
Convection Diffusion ◽  
Galerkin Finite Element Methods ◽  
Finite Element Procedure ◽  
Convection Dominated ◽  
Diffusion Problems

The weak Galerkin finite element method is combined with the method of characteristics to treat the convection-diffusion problems on the triangular mesh. The optimal order error estimates inH1andL2norms are derived for the corresponding characteristics weak Galerkin finite element procedure. Numerical tests are performed and reported.

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