Robust DPG Method for Convection-Dominated Diffusion Problems

2013 ◽  
Vol 51 (5) ◽  
pp. 2514-2537 ◽  
Author(s):  
Leszek Demkowicz ◽  
Norbert Heuer
Keyword(s):  
Convection Dominated ◽  
Diffusion Problems

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.

Finite element analysis of convection dominated reaction–diffusion problems

2004 ◽  
Vol 48 (2) ◽  
pp. 205-222 ◽  
Author(s):  
A.C. Galeão ◽  
R.C. Almeida ◽  
S.M.C. Malta ◽  
A.F.D. Loula
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Reaction Diffusion ◽  
Element Analysis ◽  
Convection Dominated ◽  
Diffusion Problems

scholarly journals A Self-Adaptive Numerical Method to Solve Convection-Dominated Diffusion Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Zhi-Wei Cao ◽  
Zhi-Fan Liu ◽  
Zhi-Feng Liu ◽  
Xiao-Hong Wang
Keyword(s):  
Numerical Solutions ◽  
Adaptive Mesh ◽  
Numerical Dissipation ◽  
Flow Problems ◽  
Special Boundary Condition ◽  
Complex Adaptive ◽  
Diffusive Term ◽  
Convection Dominated ◽  
Residual Errors ◽  
Diffusion Problems

Convection-dominated diffusion problems usually develop multiscaled solutions and adaptive mesh is popular to approach high resolution numerical solutions. Most adaptive mesh methods involve complex adaptive operations that not only increase algorithmic complexity but also may introduce numerical dissipation. Hence, it is motivated in this paper to develop an adaptive mesh method which is free from complex adaptive operations. The method is developed based on a range-discrete mesh, which is uniformly distributed in the value domain and has a desirable property of self-adaptivity in the spatial domain. To solve the time-dependent problem, movement of mesh points is tracked according to the governing equation, while their values are fixed. Adaptivity of the mesh points is automatically achieved during the course of solving the discretized equation. Moreover, a singular point resulting from a nonlinear diffusive term can be maintained by treating it as a special boundary condition. Serval numerical tests are performed. Residual errors are found to be independent of the magnitude of diffusive term. The proposed method can serve as a fast and accuracy tool for assessment of propagation of steep fronts in various flow problems.

scholarly journals A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems

2022 ◽  
pp. 110919
Author(s):  
Yu Leng ◽  
Xiaochuan Tian ◽  
Leszek Demkowicz ◽  
Hector Gomez ◽  
John T. Foster
Keyword(s):  
Galerkin Method ◽  
Convection Dominated ◽  
Diffusion Problems
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