An extended mixed finite element method for elliptic interface problems
نویسندگان
چکیده
In this paper, we propose an extended mixed finite element method for elliptic interface problems. By adding some stabilization terms, present a approximation form based on Brezzi-Douglas-Marini space and the piecewise constant function space, show that discrete inf-sup is independent of how intersects triangulation. Furthermore, derive optimal convergence holds location relative to mesh. Finally, numerical examples are presented verify our theoretical results.
منابع مشابه
Mixed Finite Element Methods for Elliptic Problems*
This paper treats the basic ideas of mixed finite element methods at an introductory level. Although the viewpoint presented is that of a mathematician, the paper is aimed at practitioners and the mathematical prerequisites are kept to a minimum. A classification of variational principles and of the corresponding weak formulations and Galerkin methods—displacement, equilibrium, and mixed—is giv...
متن کاملAn Iterative Finite Element Method for Elliptic Eigenvalue Problems
We consider the task of resolving accurately the nth eigenpair of a generalized eigenproblem rooted in some elliptic partial differential equation (PDE), using an adaptive finite element method (FEM). Conventional adaptive FEM algorithms call a generalized eigensolver after each mesh refinement step. This is not practical in our situation since the generalized eigensolver needs to calculate n e...
متن کاملAn Adaptive Finite Element Method for Linear Elliptic Problems
We propose an adaptive finite element method for linear elliptic problems based on an optimal maximum norm error estimate. The algorithm produces a sequence of successively refined meshes with a final mesh on which a given error tolerance is satisfied. In each step the refinement to be made is determined by locally estimating the size of certain derivatives of the exact solution through compute...
متن کاملL2-Error Analysis of an Isoparametric Unfitted Finite Element Method for Elliptic Interface Problems
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method was introduced which achieves a high order approximation of the geometry for domains which are implicitly described by smooth level set functions. This method ...
متن کاملPartially 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & mathematics with applications
سال: 2022
ISSN: ['0898-1221', '1873-7668']
DOI: https://doi.org/10.1016/j.camwa.2022.03.011