Least Squares Methods for Elliptic Systems

نویسندگان

  • A. K. Aziz
  • R. B. Kellogg
  • A. B. Stephens
چکیده

A weighted least squares method is given for the numerical solution of elliptic partial differential equations of Agmon-Douglis-Nirenberg type and an error analysis is provided. Some examples are given.

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

First-order System Least- Squares for Second-order Partial Diierential Equations: Part Ii. Siam J

analysis of iterative substructuring algorithms for elliptic problems in three dimensions. Least-squares mixed-nite elements for second-order elliptic problems. A least-squares approach based on a discrete minus one inner product for rst order systems. Technical report, Brookhaven National Laboratory, 1994. 4] J. H. Bramble and J. E. Pasciak. Least-squares methods for Stokes equations based on ...

متن کامل

Least-squares Proper Generalised Decompositions for Elliptic Systems

Proper generalised decompositions (PGDs) are a family of methods for efficiently solving high-dimensional PDEs. Convergence of PGD algorithms can be proven provided that the weak form of the PDE can be recast as the minimisation of some energy functional. A large number of elliptic problems, such as the Stokes problem, cannot be guaranteed to converge when employing a Galerkin PGD. Least-square...

متن کامل

Least-squares Finite Element Methods for First-order Elliptic Systems

Least-squares principles use artificial " energy " functionals to provide a Rayleigh-Ritz-like setting for the finite element method. These function-als are defined in terms of PDE's residuals and are not unique. We show that viable methods result from reconciliation of a mathematical setting dictated by the norm-equivalence of least-squares functionals with practicality constraints dictated by...

متن کامل

On Least-squares Variational Principles for the Discretization of Optimization and Control Problems

The approximate solution of optimization and control problems for systems governed by linear, elliptic partial differential equations is considered. Such problems are most often solved using methods based on the application of the Lagrange multiplier rule followed by discretization through, e.g., a Galerkin finite element method. As an alternative, we show how least-squares finite element metho...

متن کامل

Least Squares for Second Order Elliptic Problems

In this paper we introduce and analyze two least squares methods for second order elliptic di erential equations with mixed boundary conditions These methods extend to problems which involve oblique derivative boundary conditions as well as nonsym metric and inde nite problems as long as the original problem has a unique solution With the methods to be developed Neumann and oblique boundary con...

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 2010