Abstract
AbstractThis paper deals with the numerical analysis for a family of nonlinear degenerate parabolic problems. The model is spatially discretized using a finite element method; an implicit Euler scheme is employed for time discretization. We deduce sufficient conditions to ensure that the fully discrete problem has a unique solution and to prove quasi-optimal error estimates for the approximation. Finally, we propose a nonlinear degenerate parabolic problem that arises from electromagnetic applications in conductive nonlinear magnetic media and deduce its solubility and convergence by using the developed abstract theory, including some numerical results to confirm the obtained theoretical results.
Funder
Universidad del Cauca
Ministerio de Ciencias - Minciencias
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics
Reference25 articles.
1. Paronetto, F.: Homogenization of degenerate elliptic-parabolic equations. Asymptot. Anal. 37(1), 21–56 (2004)
2. Showalter, R.: Monotone operators in Banach space and nonlinear partial differential equations, vol. 49. American Mathematical Society, Providence (1997)
3. Zlamal, M.: Finite element solution of quasistationary nonlinear magnetic field. ESAIM: Mathematical Modelling and Numerical Analysis -Modélisation Mathématique et Analyse Numérique 16(2), 161–191 (1982)
4. MacCamy, R.C., Suri, M.: A time-dependent interface problem for twodimensional eddy currents. Quart. Appl. Math. 44(4), 675–690 (1987). https://doi.org/10.1090/qam/872820
5. Bermúdez, A., Reales, C., Rodríguez, R., Salgado, P.: Numerical analysis of a transient eddy current axisymmetric problem involving velocity terms. Numer. Methods Partial Differential Equations 28(3), 984–1012 (2012). https://doi.org/10.1002/num.20670
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献