scholarly journals Defect-deferred correction method for the two-domain convection-dominated convection–diffusion problem

2017 ◽  
Vol 450 (1) ◽  
pp. 180-196 ◽  
Author(s):  
Dilek Erkmen ◽  
Alexander E. Labovsky
Keyword(s):  
Correction Method ◽  
Diffusion Problem ◽  
Deferred Correction ◽  
Convection Diffusion ◽  
Convection Dominated

A VISCOUS-INVISCID COUPLING UNDER MIXED BOUNDARY CONDITIONS

1992 ◽  
Vol 02 (04) ◽  
pp. 461-482 ◽  
Author(s):  
C. CANUTO ◽  
A. RUSSO
Keyword(s):  
Boundary Conditions ◽  
Original Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Diffusion Problem ◽  
Convection Diffusion ◽  
Convection Equation ◽  
Convection Dominated

In this paper we consider a nonlinear modification of a linear convection-diffusion problem in order to get a pure convection equation where the original problem is convection dominated. We extend the results of previous papers by considering mixed Dirichlet/Oblique derivative boundary conditions.

A Defect Correction Method for the Evolutionary Convection — Diffusion Problem with Increased Time Accuracy

2009 ◽  
Vol 9 (2) ◽  
pp. 154-164 ◽  
Author(s):  
A. LABOVSKY
Keyword(s):  
Computational Cost ◽  
Correction Method ◽  
Diffusion Problem ◽  
Stability Factor ◽  
Defect Correction ◽  
Convection Diffusion ◽  
Viscosity Parameter ◽  
Correction Step ◽  
The Right ◽  
Time Accuracy

AbstractThis work presents a defect correction method with increased time accuracy. The desired time accuracy is attained with no extra computational cost. The method is applied to the evolutionary transport problem, and is proven to be unconditionally stable. In the defect step, the artificial viscosity parameter is added to the Peclet number as a stability factor, and the system is antidiffused in the correction step. The time accuracy is also increased in the correction step by modifying the right hand side.Computational results verifying the claimed space and time accuracy of the approximate solution are presented.

scholarly journals A Finite Element Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Vidar Thomée
Keyword(s):  
Finite Element ◽  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Euler Approximation ◽  
Convection Diffusion ◽  
Time Stepping ◽  
Backward Euler ◽  
Spatially Periodic ◽  
Forward Euler

AbstractFor a spatially periodic convection-diffusion problem, we analyze a time stepping method based on Lie splitting of a spatially semidiscrete finite element solution on time steps of length k, using the backward Euler method for the diffusion part and a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {k/m} for the convection part. This complements earlier work on time splitting of the problem in a finite difference context.

scholarly journals A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 769-782
Author(s):  
Amiya K. Pani ◽  
Vidar Thomée ◽  
A. S. Vasudeva Murthy
Keyword(s):  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Second Order ◽  
Time Step ◽  
Convection Diffusion ◽  
First Order ◽  
Backward Euler ◽  
Strang Splitting ◽  
Spatially Periodic

AbstractWe analyze a second-order in space, first-order in time accurate finite difference method for a spatially periodic convection-diffusion problem. This method is a time stepping method based on the first-order Lie splitting of the spatially semidiscrete solution. In each time step, on an interval of length k, of this solution, the method uses the backward Euler method for the diffusion part, and then applies a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {\frac{k}{m}} for the convection part. With h the mesh width in space, this results in an error bound of the form {C_{0}h^{2}+C_{m}k} for appropriately smooth solutions, where {C_{m}\leq C^{\prime}+\frac{C^{\prime\prime}}{m}}. This work complements the earlier study [V. Thomée and A. S. Vasudeva Murthy, An explicit-implicit splitting method for a convection-diffusion problem, Comput. Methods Appl. Math. 19 2019, 2, 283–293] based on the second-order Strang splitting.

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