scholarly journals Discontinuous Galerkin Approximation of Relaxation Models for Linear and Nonlinear Diffusion Equations

2012 ◽  
Vol 34 (1) ◽  
pp. A105-A136 ◽  
Author(s):  
Fausto Cavalli ◽  
Giovanni Naldi ◽  
Ilaria Perugia
Keyword(s):  
Discontinuous Galerkin ◽  
Nonlinear Diffusion ◽  
Galerkin Approximation ◽  
Diffusion Equations ◽  
Nonlinear Diffusion Equations ◽  
Linear And Nonlinear ◽  
Relaxation Models

scholarly journals Flux form Semi-Lagrangian methods for parabolic problems

2016 ◽  
Vol 7 (3) ◽  
pp. 56-73
Author(s):  
Luca Bonaventura ◽  
Roberto Ferretti
Keyword(s):  
Stability Analysis ◽  
Nonlinear Diffusion ◽  
Diffusion Equations ◽  
Parabolic Problems ◽  
Nonlinear Diffusion Equations ◽  
Nonlinear Parabolic Problems ◽  
Numerical Examples ◽  
Advection Diffusion ◽  
Nonlinear Parabolic ◽  
Linear And Nonlinear

Abstract A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and stability analysis is proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection diffusion and nonlinear parabolic problems.

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