Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures

1982 ◽  
Vol 19 (5) ◽  
pp. 871-885 ◽  
Author(s):  
Jim Douglas, Jr. ◽  
Thomas F. Russell
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
Finite Difference ◽  
Method Of Characteristics ◽  
The Method Of Characteristics ◽  
Convection Dominated ◽  
Diffusion Problems

scholarly journals Domain Decomposition Modified with Characteristic Mixed Finite Element and Numerical Analysis for Three-Dimensional Slightly Compressible Oil-Water Seepage Displacement

2017 ◽  
Vol 9 (1) ◽  
pp. 143
Author(s):  
Yirang Yuan ◽  
Luo Chang ◽  
Changfeng Li ◽  
Tongjun Sun
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Method Of Characteristics ◽  
Mixed Finite Element ◽  
Three Dimensional ◽  
Optimal Error Estimate ◽  
Computational Domain ◽  
Time Step ◽  
Slightly Compressible ◽  
The Method Of Characteristics

A parallel algorithm is presented to solve three-dimensional slightly compressible seepage displacement where domain decomposition and characteristics-mixed finite element are combined. Decomposing the computational domain into several subdomains, we define a special function to approximate the derivative at interior boundary explicitly and obtain numerical solutions of the saturation implicitly on subdomains in parallel. The method of characteristics can confirm strong stability at the fronts, and can avoid numerical dispersion and nonphysical oscillation. It can adopt large-time step but can obtain small time truncation error. So a characteristic domain decomposition finite element scheme is put forward to compute the saturation. The flow equation is computed by the method of mixed finite element and numerical accuracy of Darcy velocity is improved one order. For a model problem we apply some techniques such as variation form, domain decomposition, the method of characteristics, the principle of energy, negative norm estimates, induction hypothesis, and the theory of priori estimates of differential equations to derive optimal error estimate in $l^2$ norm. Numerical example is given to testify theoretical analysis and numerical data show that this method is effective in solving actual applications. Then it can solve the well-known problem.

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
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