scholarly journals An Obstacle Problem for Noncoercive Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Luigi Greco ◽  
Gioconda Moscariello ◽  
Gabriella Zecca
Keyword(s):  
Nonlinear Equations ◽  
Obstacle Problem ◽  
Second Order ◽  
Convection Term ◽  
Marcinkiewicz Space ◽  
Growth Coefficient ◽  
Stationary Diffusion ◽  
Convection Problem ◽  
Diffusion Convection

We study the obstacle problem for second order nonlinear equations whose model appears in the stationary diffusion-convection problem. We assume that the growth coefficient of the convection term lies in the Marcinkiewicz spaceweak-LN.

Stability-Controllable Second-order Difference scheme for convection term

1998 ◽  
Vol 7 (2) ◽  
pp. 119-130 ◽  
Author(s):  
Ming-Jiu Ni ◽  
Wen-Quan Tao ◽  
Shang-Jin Wang
Keyword(s):  
Difference Scheme ◽  
Second Order ◽  
Convection Term ◽  
Order Difference

scholarly journals SUPG-stabilized virtual elements for diffusion-convection problems: a robustness analysis

2021 ◽  
Author(s):  
Lourenco Beirao da Veiga ◽  
Franco Dassi ◽  
Carlo Lovadina ◽  
Giuseppe Vacca
Keyword(s):  
Robustness Analysis ◽  
Mesh Size ◽  
Original Method ◽  
Convection Term ◽  
Multiplicative Factor ◽  
Numerical Result ◽  
Virtual Element Methods ◽  
Virtual Element ◽  
Diffusion Convection ◽  
Convection Dominated

The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced in [Benedetto et al, CMAME 2016] we are able to show an “almost uniform” error bound (in the sense that the unique term that depends in an unfavourable way on the parameters is damped by a higher order mesh-size multiplicative factor). We also introduce a novel discretization of the convection term that allows us to develop error estimates that are fully robust in the convection dominated cases. We finally present some numerical result.

scholarly journals Adaptive ADI Numerical Analysis of 2D Quenching-Type Reaction: Diffusion Equation with Convection Term

2020 ◽  
Vol 2020 ◽  
pp. 1-19 ◽  
Author(s):  
Xiaoliang Zhu ◽  
Yongbin Ge
Keyword(s):  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Adaptive Mesh ◽  
Second Order ◽  
High Order ◽  
Reaction Diffusion Equation ◽  
Convection Term ◽  
Central Difference ◽  
High Order Scheme ◽  
Singular Parabolic Equation

An adaptive high-order difference solution about a 2D nonlinear degenerate singular reaction-diffusion equation with a convection term is initially proposed in the paper. After the first and the second central difference operator approximating the first-order and the second-order spatial derivative, respectively, the higher-order spatial derivatives are discretized by applying the Taylor series rule and the temporal derivative is discretized by using the Crank–Nicolson (CN) difference scheme. An alternating direction implicit (ADI) scheme with a nonuniform grid is built in this way. Meanwhile, accuracy analysis declares the second order in time and the fourth order in space under certain conditions. Sequentially, the high-order scheme is performed on an adaptive mesh to demonstrate quenching behaviors of the singular parabolic equation and analyse the influence of combustion chamber size on quenching. The paper displays rationally that the proposed scheme is practicable for solving the 2D quenching-type problem.

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