论文信息 - Finite element solution of nonlinear diffusion problems

Finite element solution of nonlinear diffusion problems

Abstract In this paper we describe the Rothe-finite element numerical scheme to find an approximate solution of a nonlinear diffusion problem modeled as a parabolic partial differential equation of even order. This scheme is based on the Rothe’s approximation in time and on the finite element method (FEM) approximation in the spatial discretization. A proof of convergence of the approximate solution is given and error estimates are shown.

M. S. El-Azab | K. M. Abdelgaber | M. El-Azab

[1] M. El-Azab. An effective linear scheme to solve nonlinear degenerate parabolic differential equations , 2003 .

[2] M. S. El-Azab. An approximation scheme for a nonlinear diffusion Fisher's equation , 2007, Appl. Math. Comput..

[3] I. Kazada. Finite element techniques in groundwater flow studies: with applications in hydraulic and geotechnical engineering. , 1990 .

[4] E. Kreyszig. Introductory Functional Analysis With Applications , 1978 .

[5] J. Bear. Dynamics of Fluids in Porous Media , 1975 .

[6] Manil Suri,et al. A posteriori estimation of the linearization error for strongly monotone nonlinear operators , 2007 .

[7] Angus E. Taylor. Introduction to functional analysis , 1959 .

[8] I. Babuska,et al. Finite Element Analysis , 2021 .

[9] Ivo Babuška,et al. A POSTERIORI ERROR ESTIMATION FOR THE FINITE ELEMENT METHOD-OF-LINES SOLUTION OF PARABOLIC PROBLEMS , 1999 .

[10] J. Hoffman. Numerical Methods for Engineers and Scientists , 2018 .

[11] I. Babuska,et al. A‐posteriori error estimates for the finite element method , 1978 .

[12] M. S. El-Azab. Solution of nonlinear transport-diffusion problems by linearization , 2007, Appl. Math. Comput..

[13] J. Z. Zhu,et al. The finite element method , 1977 .