scholarly journals Analysis of total variation flow and its finite element approximations

2003 ◽  
Vol 37 (3) ◽  
pp. 533-556 ◽  
Author(s):  
Xiaobing Feng ◽  
Andreas Prohl
Keyword(s):  
Finite Element ◽  
Total Variation ◽  
Finite Element Approximations ◽  
Total Variation Flow

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

scholarly journals 3D Unsteady Diffusion and Reaction-Diffusion with Singularities by GFEM with 27-Node Hexahedrons

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Estaner Claro Romão
Keyword(s):  
Finite Element ◽  
Variable Temperature ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Third Order ◽  
Order Of Accuracy ◽  
Finite Element Approximations ◽  
Temperature Solution ◽  
The One ◽  
Primary Variable

The Galerkin Finite Element Method (GFEM) with 8- and 27-node hexahedrons elements is used for solving diffusion and transient three-dimensional reaction-diffusion with singularities. Besides analyzing the results from the primary variable (temperature), the finite element approximations were used to find the derivative of the temperature in all three directions. This technique does not provide an order of accuracy compatible with the one found in the temperature solution; thereto, a calculation from the third order finite differences is proposed here, which provide the best results, as demonstrated by the first two applications proposed in this paper. Lastly, the presentation and the discussion of a real application with two cases of boundary conditions with singularities are proposed.

scholarly journals On the Adaptive Selection of the Parameter in Stabilized Finite Element Approximations

2013 ◽  
Vol 51 (3) ◽  
pp. 1585-1609 ◽  
Author(s):  
Mark Ainsworth ◽  
Alejandro Allendes ◽  
Gabriel R. Barrenechea ◽  
Richard Rankin
Keyword(s):  
Finite Element ◽  
Adaptive Selection ◽  
Stabilized Finite Element ◽  
Finite Element Approximations ◽  
Selection Of
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