A priori error estimates for upwind finite volume schemes for two-dimensional linear convection diffusion problems

2016 ◽  
Vol 47 (2) ◽  
pp. 473-488
Author(s):  
Dietmar Kröner ◽  
Mirko Rokyta
Keyword(s):  
Error Estimates ◽  
Finite Volume ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Two Dimensional ◽  
Finite Volume Schemes ◽  
Convection Diffusion ◽  
Priori Error Estimates ◽  
Diffusion Problems

scholarly journals A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yang Liu ◽  
Hong Li ◽  
Wei Gao ◽  
Siriguleng He ◽  
Zhichao Fang
Keyword(s):  
Error Estimates ◽  
Mixed Method ◽  
Mixed Finite Element ◽  
A Priori ◽  
A Priori Error Estimates ◽  
The Novel ◽  
Convection Diffusion ◽  
Backward Euler ◽  
Priori Error Estimates ◽  
Diffusion Problems

A novel characteristic expanded mixed finite element method is proposed and analyzed for reaction-convection-diffusion problems. The diffusion term∇·(a(x,t)∇u)is discretized by the novel expanded mixed method, whose gradient belongs to the square integrable space instead of the classicalH(div;Ω)space and the hyperbolic partd(x)(∂u/∂t)+c(x,t)·∇uis handled by the characteristic method. For a priori error estimates, some important lemmas based on the novel expanded mixed projection are introduced. The fully discrete error estimates based on backward Euler scheme are obtained. Moreover, the optimal a priori error estimates inL2- andH1-norms for the scalar unknownuand a priori error estimates in(L2)2-norm for its gradientλand its fluxσ(the coefficients times the negative gradient) are derived. Finally, a numerical example is provided to verify our theoretical results.

Error estimates for higher-order finite volume schemes for convection–diffusion problems

2018 ◽  
Vol 26 (1) ◽  
pp. 35-62
Author(s):  
Dietmar Kröner ◽  
Mirko Rokyta
Keyword(s):  
Error Estimates ◽  
Finite Volume ◽  
Original Problem ◽  
A Priori ◽  
Higher Order ◽  
Finite Volume Schemes ◽  
Convection Diffusion ◽  
Type Reconstruction ◽  
Convection Dominated ◽  
Diffusion Problems

AbstractIt is still an open problem to provea priorierror estimates for finite volume schemes of higher order MUSCL type, including limiters, on unstructured meshes, which show some improvement compared to first order schemes. In this paper we use these higher order schemes for the discretization of convection dominated elliptic problems in a convex bounded domainΩin ℝ2and we can prove such kind of ana priorierror estimate. In the part of the estimate, which refers to the discretization of the convective term, we gainh1/2. Although the original problem is linear, the numerical problem becomes nonlinear, due to MUSCL type reconstruction/limiter technique.

scholarly journals A note on a priori error estimates for augmented mixed methods

2016 ◽  
Vol 57 ◽  
pp. 139-144
Author(s):  
Tomás P. Barrios ◽  
Edwin Behrens ◽  
Rommel Bustinza
Keyword(s):  
Mixed Methods ◽  
Error Estimates ◽  
A Priori ◽  
A Priori Error Estimates ◽  
Priori Error Estimates
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