Piecewise Bilinear Preconditioning on High-order Finite Element Methods

نویسندگان

  • SANG DONG KIM
  • S. D. KIM
چکیده

The bounds of eigenvalues which are independent of both degrees of high-order elements and mesh sizes are shown for the preconditioned system by bilinear elements for the highorder finite elements discretizations applied to a model uniformly elliptic operator.

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

Piecewise Bilinear Preconditioning of High-order Finite Element Methods

PIECEWISE BILINEAR PRECONDITIONING OF HIGH-ORDER FINITE ELEMENT METHODS SANG DONG KIM Abstract. Bounds on eigenvalues which are independent of both degrees of high-order elements and mesh sizes are shown for the system preconditioned by bilinear elements for high-order finite element discretizations applied to a model uniformly elliptic operator.

متن کامل

Are Bilinear Quadrilaterals Better Than Linear Triangles?

This paper compares the theoretical effectiveness of bilinear approximation over quadrilaterals with linear approximation over triangles. Anisotropic mesh transformation is used to generate asymptotically optimally efficient meshes for piecewise linear interpolation over triangles and bilinear interpolation over quadrilaterals. For approximating a convex function, although bilinear quadrilatera...

متن کامل

Multilevel Boundary Functionals for Least-squares Mixed Finite Element Methods

For least-squares mixed nite element methods for the rst-order system formulation of second-order elliptic problems, a technique for the weak enforcement of boundary conditions is presented. This approach is based on least-squares boundary functionals which are equivalent to the H ?1=2 and H 1=2 norms on the trace spaces of lowest-order Raviart-Thomas elements for the ux and standard continuous...

متن کامل

On the Asymptotic Spectrum of Finite Element Matrix Sequences

We derive a new formula for the asymptotic eigenvalue distribution of stiffness matrices obtained by applying P1 Finite Elements with standard mesh refinement to the semi elliptic PDE of second order in divergence form −∇(K∇Tu) = f on Ω, u = g on ∂Ω. Here Ω ⊂ R and K is supposed to be piecewise continuous and pointwise symmetric semi positive definite. The symbol describing this asymptotic eige...

متن کامل

Analysis of Some Mixed Finite Element Methods Related to Reduced Integration

We prove error estimates for the following two mixed finite element methods related to reduced integration: A method for Stokes' problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure, and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants f...

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 2006