Efficient expanded mixed finite element method for the quasilinear elliptic problems

With the rapid development of computing power, advanced modelling and numerical simulation technology has become a useful and powerful tool. Some efficient numerical methods are presented. In this article, expanded mixed finite element method is introduced to solve the quasilinear elliptic problems. This method expands the traditional mixed finite element method in the sense that three variables are explicitly treated simultaneously. Existence and uniqueness of the discrete approximation are demonstrated. L

[1]  Hongxing Rui,et al.  A Block-Centered Finite Difference Method for the Darcy-Forchheimer Model , 2012, SIAM J. Numer. Anal..

[2]  N. Heuer,et al.  On the numerical analysis of nonlinear twofold saddle point problems , 2003 .

[3]  Burhan Khurshid,et al.  Technology optimized fixed-point bit-parallel multiplier for LUT based FPGAs , 2015, 2015 2nd International Conference on Electronics and Communication Systems (ICECS).

[4]  Rodrigo Weber dos Santos,et al.  A parallel accelerated adaptive mesh algorithm for the solution of electrical models of the heart , 2012, Int. J. High Perform. Syst. Archit..

[5]  M. Fortin,et al.  E cient rectangular mixed fi-nite elements in two and three space variables , 1987 .

[6]  Luigi Raffo,et al.  A fast MPI-based parallel framework for cycle-accurate HDL multi-parametric simulations , 2010, Int. J. High Perform. Syst. Archit..

[7]  Victor Ginting,et al.  Finite-volume-element method for second-order quasilinear elliptic problems , 2011 .

[8]  V. Thomée,et al.  Error estimates for some mixed finite element methods for parabolic type problems , 1981 .

[9]  Jean E. Roberts,et al.  Global estimates for mixed methods for second order elliptic equations , 1985 .

[10]  G. Gatica,et al.  A priori and a posteriori error analyses of augmented twofold saddle point formulations for nonlinear elasticity problems , 2013 .

[11]  M. Wheeler,et al.  Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Cell-Centered Finite Differences , 1997 .

[12]  F. Brezzi.  On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers , 1974 .

[13]  Bodo Heise.  Analysis of a fully discrete finite element method for a nonlinear magnetic field problem , 1994 .

[14]  John W. Barrett,et al.  Finite element approximation of some degenerate monotone quasilinear elliptic systems , 1996 .

[15]  Eun-Jae Park.  Mixed finite element methods for generalized Forchheimer flow in porous media , 2005 .

[16]  Zhangxin Chen,et al.  Expanded mixed finite element methods for linear second-order elliptic problems, I , 1998 .

[17]  Hongxing Rui,et al.  Mixed Element Method for Two-Dimensional Darcy-Forchheimer Model , 2012, J. Sci. Comput..

[18]  R. S. Falk,et al.  Error estimates for mixed methods , 1980 .

[19]  L. D. Marini,et al.  Two families of mixed finite elements for second order elliptic problems , 1985 .

[20]  Todd Arbogast,et al.  Enhanced Cell-Centered Finite Differences for Elliptic Equations on General Geometry , 1998, SIAM J. Sci. Comput..

[21]  Keivan Navi,et al.  New fully single layer QCA full-adder cell based on feedback model , 2015, Int. J. High Perform. Syst. Archit..

[22]  Gabriel N. Gatica,et al.  Analysis of an augmented pseudostress-based mixed formulation for a nonlinear Brinkman model of porous media flow , 2015 .

[23]  Ricardo G. Durán.  Error analysis in $L^p \leqslant p \leqslant \infty $ , for mixed finite element methods for linear and quasi-linear elliptic problems , 1988 .

[24]  Mary F. Wheeler,et al.  Numerical discretization of a Darcy–Forchheimer model , 2008, Numerische Mathematik.

[25]  Eun-Jae Park,et al.  A mixed finite element method for a strongly nonlinear second-order elliptic problem , 1995 .

[26]  A. I. Garralda-Guillem,et al.  A posteriori error analysis of twofold saddle point variational formulations for nonlinear boundary value problems , 2014 .

[27]  Italo Epicoco,et al.  The performance model for a parallel SOR algorithm using the red-black scheme , 2012, Int. J. High Perform. Syst. Archit..

[28]  Fabio Milner,et al.  Mixed finite element methods for quasilinear second-order elliptic problems , 1985 .

[29]  J. Douglas,et al.  Prismatic mixed finite elements for second order elliptic problems , 1989 .

[30]  Kwang Y. Kim.  Mixed finite volume method for nonlinear elliptic problems , 2005 .

[31]  P. Raviart,et al.  A mixed finite element method for 2-nd order elliptic problems , 1977 .