论文信息 - Discontinuous Galerkin approximation with discrete variational principle for the nonlinear Laplacian

Discontinuous Galerkin approximation with discrete variational principle for the nonlinear Laplacian

A discontinuous Galerkin method is analyzed to approximate the nonlinear Laplacian model problem. The salient feature of the proposed scheme is that it is endowed with a discrete variational principle. The convergence of the discrete approximations to the exact solution is proven. To cite this article: E. Burman, A. Ern, C R. Acad. Sci. Paris, Ser. I 346 (2008). (C) 2008 Academie des sciences.

Alexandre Ern | Erik Burman | A. Ern | E. Burman

[1] Philippe G. Ciarlet,et al. The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[2] Gabriel N. Gatica,et al. A Local Discontinuous Galerkin Method for Nonlinear Diffusion Problems with Mixed Boundary Conditions , 2004, SIAM J. Sci. Comput..

[3] John W. Barrett,et al. Finite element approximation of the p-Laplacian , 1993 .

[4] R. Glowinski,et al. Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires , 1975 .

[5] S. Chow. Finite element error estimates for non-linear elliptic equations of monotone type , 1989 .

[6] Adrian J. Lew,et al. Discontinuous Galerkin methods for non‐linear elasticity , 2006 .

[7] Wenbin Liu,et al. Quasi-norm a priori and a posteriori error estimates for the nonconforming approximation of p-Laplacian , 2001, Numerische Mathematik.