Optimal convergence analysis of an immersed interface finite element method

نویسندگان

  • So-Hsiang Chou
  • Do Y. Kwak
  • Kye T. Wee
چکیده

We analyze an immersed interface finite element method based on linear polynomials on noninterface triangular elements and piecewise linear polynomials on interface triangular elements. The flux jump condition is weakly enforced on the smooth interface. Optimal error estimates are derived in the broken H1-norm and L2-norm.

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 partially penalty immersed Crouzeix-Raviart finite element method for interface problems

The elliptic equations with discontinuous coefficients are often used to describe the problems of the multiple materials or fluids with different densities or conductivities or diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in which the diffusion coefficient is a piecewise definite-positive matri...

متن کامل

Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions

In this work, a class of new finite-element methods, called immersed-interface finite-element methods, is developed to solve elliptic interface problems with nonhomogeneous jump conditions. Simple non–body-fitted meshes are used. A single function that satisfies the same nonhomogeneous jump conditions is constructed using a level-set representation of the interface. With such a function, the di...

متن کامل

Higher Degree Immersed Finite Element Methods for Second-order Elliptic Interface Problems

We present higher degree immersed finite element (IFE) spaces that can be used to solve two dimensional second order elliptic interface problems without requiring the mesh to be aligned with the material interfaces. The interpolation errors in the proposed piecewise p degree spaces yield optimal O(hp+1) and O(h) convergence rates in the L2 and broken H1 norms, respectively, under mesh refinemen...

متن کامل

The Immersed Finite Volume Element Method for Some Interface Problems with Nonhomogeneous Jump Conditions

In this paper, an immersed finite volume element (IFVE) method is developed for solving some interface problems with nonhomogeneous jump conditions. Using the source removal technique of nonhomogeneous jump conditions, the new IFVE method is the finite volume element method applied to the equivalent interface problems with homogeneous jump conditions and have properties of the usual finite volu...

متن کامل

Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems

This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods contain extra stabilization terms introduced only at interface edges for penalizing the discontinuity in IFE functions. With the enhanced stability due to the ...

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:
  • Adv. Comput. Math.

دوره 33  شماره 

صفحات  -

تاریخ انتشار 2010