Hybridizing Raviart-thomas Elements for the Helmholtz Equation

نویسندگان

  • P. Monk
  • J. Schöberl
  • A. Sinwel
  • PETER MONK
  • JOACHIM SCHÖBERL
  • ASTRID SINWEL
چکیده

This paper deals with the application of hybridized mixed methods for discretizing the Helmholtz problem. Starting from a mixed formulation, where the flux is considered a separate unknown, we use Raviart-Thomas finite elements to approximate the solution. We present two ways of hybridizing the problem, which means breaking the normal continuity of the fluxes and then imposing continuity weakly via functions supported on the element faces or edges. The first method is the Ultra-Weak Variational Formulation, first introduced by Cessenat and Després [7]; the second one uses Lagrange multipliers on element interfaces. We compare the two methods, and give numerical results. We observe that the iterative solvers applied to the two methods behave well for large wave numbers.

برای دانلود رایگان 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 Hybridized Crouziex-Raviart Nonconforming Finite Element and Discontinuous Galerkin Method for a Two-Phase Flow in the Porous Media

In this study, we present a numerical solution for the two-phase incompressible flow in the porous media under isothermal condition using a hybrid of the linear lower-order nonconforming finite element and the interior penalty discontinuous Galerkin (DG) method. This hybridization is developed for the first time in the two-phase modeling and considered as the main novelty of this research.The p...

متن کامل

Numerische Simulation Auf Massiv Parallelen Rechnern Crouzeix-raviart Type Nite Elements on Anisotropic Meshes

The paper deals with a non-conforming nite element method on a class of anisotropic meshes. The Crouzeix-Raviart element is used on triangles and tetrahedra. For rectangles and prismatic (pentahedral) elements a novel set of trial functions is proposed. Anisotropic local interpolation error estimates are derived for all these types of element and for functions from classical and weighted Sobole...

متن کامل

Equilibrated residual error estimator for edge elements

Reliable a posteriori error estimates without generic constants can be obtained by a comparison of the finite element solution with a feasible function for the dual problem. A cheap computation of such functions via equilibration is well known for scalar equations of second order. We simplify and modify the equilibration such that it can be applied to the curl-curl equation and edge elements. T...

متن کامل

Rehabilitation of the Lowest-Order Raviart-Thomas Element on Quadrilateral Grids

A recent study [4] reveals that convergence of finite element methods usingH(div ,Ω)compatible finite element spaces deteriorates on non-affine quadrilateral grids. This phenomena is particularly troublesome for the lowest-order Raviart-Thomas elements, because it implies loss of convergence in some norms for finite element solutions of mixed and least-squares methods. In this paper we propose ...

متن کامل

A new coupling of mixed finite element and boundary element methods for an exterior Helmholtz problem in the plane

This paper deals with the scattering of time harmonic electromagnetic waves by an infinitely long cylinder containing a non-homogeneous conducting medium. More precisely, we study the transverse magnetic field that solves an interface problem holding between the cross section of the cylinder and the exterior two-dimensional free space. We apply a dual-mixed variational formulation in the obstac...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008