A Finite Volume Element Method for a Nonlinear Parabolic Problem
We study a finite volume element discretization of a nonlinear parabolic equation in a convex polygonal domain. We show the existence of the discrete solution and derive error estimates in L 2- and H 1-norms. We also consider a linearized method and provide numerical results to illustrate our theoretical findings.
KeywordsNonlinear parabolic problem Finite volume element method Error estimates
The research of P. Chatzipantelidis was partly supported by the FP7-REGPOT-2009-1 project “Archimedes Center for Modeling Analysis and Computation,” funded by the European Commission. The research of V. Ginting was partially supported by the grants from DOE (DE-FE0004832 and DE-SC0004982), the Center for Fundamentals of Subsurface Flow of the School of Energy Resources of the University of Wyoming (WYDEQ49811GNTG, WYDEQ49811PER), and from NSF (DMS-1016283).
- 5.Eymard, R., Gallouët, T., Herbin, R.: Finite volume methods. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, vol. VII, pp. 713–1020. North-Holland, Amsterdam (2000)Google Scholar
- 7.Ladyženskaja, O.A., Solonnikov, V.A., Uraĺceva, N.N.: Linear and Quasilinear Equations of Parabolic Type. Translated from the Russian by S. Smith. American Mathematical Society, Providence (1968)Google Scholar