Analysis of Total Variation Flow and Its Finite Element Approximations

@inproceedings{Feng2002AnalysisOT,
  title={Analysis of Total Variation Flow and Its Finite Element Approximations},
  author={Xiaobing Feng and Andreas Prohl},
  year={2002}
}
We study the gradient flow for the total variation functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow, and establish well-posedness of the problem by the energy method. The main idea of our approach is to exploit the relationship between the regularized gradient flow (characterized by a small positive parameter ε, see (1.7)) and the minimal surface flow [21] and the prescribed mean curvature flow… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 27 references

Pseudosolutions of the time-dependent minimal surface problem

A. Lichnewsky, R. Temam
J. Differential Equations • 1978
View 16 Excerpts
Highly Influenced

Evolutionary surfaces of prescribed mean curvature

C. Gerhardt
J. Differential Equations • 1980
View 10 Excerpts
Highly Influenced

Minimal surfaces and functions of bounded variation

E. Giusti
Birkhäuser Verlag, Basel • 1984
View 4 Excerpts
Highly Influenced

Mazón, Some qualitative properties for the total variation flow

F. Andreu, V. Caselles, J.M.J.I. Dı́az
J. Funct. Anal • 2002
View 1 Excerpt

Trudinger, Elliptic partial differential equations of second order

N.S.D. Gilbarg
Reprint of the 1998 ed • 2001
View 3 Excerpts

Applications to nonlinear partial differential equations and Hamiltonian systems, in Variational methods

M. Struwe
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics (Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics), • 2000
View 1 Excerpt

Regularization by functions of bounded variation and applications to image enhancement

E. Casas, K. Kunisch, C. Pola
Appl. Math. Optim • 1999

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