Applications of approximate gradient schemes for nonlinear parabolic equations
- 121 Downloads
We develop gradient schemes for the approximation of the Perona-Malik equations and nonlinear tensor-diffusion equations. We prove the convergence of these methods to the weak solutions of the corresponding nonlinear PDEs. A particular gradient scheme on rectangular meshes is then studied numerically with respect to experimental order of convergence which shows its second order accuracy. We present also numerical experiments related to image filtering by time-delayed Perona-Malik and tensor diffusion equations.
Keywordsregularized Perona-Malik equation gradient schemes
MSC 201065M08 65M12
Unable to display preview. Download preview PDF.
- R. Eymard, T. Gallouët, R. Herbin: Finite volume methods. Handbook of numerical analysis. Vol. 7: Solution of equations in Rn (Part 3) (P. G. Ciarlet et al., eds.). Techniques of scientific computing (Part 3), North Holland/Elsevier, Amsterdam, 2000, pp. 713–1020.Google Scholar
- R. Eymard, R. Herbin: Gradient scheme approximations for diffusion problems. Finite Volumes for Complex Applications 6: Problems and Perspectives. Vol. 1, 2. Conf. Proc. (J. Fořt et al., eds.). Proceedings in Mathematics 4, Springer, Heidelberg, 2011, pp. 439–447.Google Scholar