Mixed finite element methods for quasilinear second order elliptic problems : the p-version

نویسندگان

  • F. A. MILNER
  • M. SURI
چکیده

The p-version of the finite element method is analyzed for quasilinear second order elhptic problems in mixed weak form Approximation properties of the Raviart-Thomas projection are demonstrated and L-error bounds for the three relevant variables in the mixed method are denved Résumé — Nous analysons la version-p de la méthode d'éléments finis mixtes pour des problèmes quasihnéaires elliptiques du second ordre en forme faible mixte Nous démontrons des propriétés d'approximation de la projection de Raviart-Thomas et on dérive des bornes de V erreur dans L (O ) pour les trois variables d'intérêt dans la méthode mixte

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A-posteriori error analysis of hp-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic problems

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximat...

متن کامل

Expanded mixed finite element methods for quasilinear second order elliptic problems, II

A new mixed formulation recently proposed for linear problems is extended to quasilinear second order elliptic problems This new formulation expands the standard mixed formulation in the sense that three variables are explicitly treated i e the scalar unknown its gradient and its ux the coe cients times the gradient Based on this formulation mixed nite element approximations of the quasilinear ...

متن کامل

On the Stability and Convergence of Higher-order Mixed Finite Element Methods for Second-order Elliptic Problems

We investigate the use of higher-order mixed methods for secondorder elliptic problems by establishing refined stability and convergence estimates which take into account both the mesh size h and polynomial degree p . Our estimates yield asymptotic convergence rates for the pand h p-versions of the finite element method. They also describe more accurately than previously proved estimates the in...

متن کامل

The effect of numerical integration in nonmonotone nonlinear elliptic problems with application to numerical homogenization methods

A finite element method with numerical quadrature is considered for the solution of a class of second-order quasilinear elliptic problems of nonmonotone type. Optimal a priori error estimates for the H and the L norms are derived. The uniqueness of the finite element solution is established for a sufficiently fine mesh. Application to numerical homogenization methods is considered.

متن کامل

Asymptotic Expansions and Extrapolation of Approximate Eigenvalues for Second Order Elliptic Problems by Mixed Finite Element Methods

In this paper, we derive an asymptotic error expansion for the eigenvalue approximations by the lowest order Raviart-Thomas mixed finite element method for the general second order elliptic eigenvalue problems. Extrapolation based on such an expansion is applied to improve the accuracy of the eigenvalue approximations. Furthermore, we also prove the superclose property between the finite elemen...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009