P1-Nonconforming Finite Elements on Triangulations into Triangles and Quadrilaterals
نویسندگان
چکیده
The P1-nonconforming finite element is introduced for arbitrary triangulations into quadrilaterals and triangles of multiple connected Lipschitz domains. An explicit a priori analysis for the combination of the Park–Sheen and the Crouzeix–Raviart nonconforming finite element methods is given for second-order elliptic PDEs with inhomogeneous Dirichlet boundary conditions.
منابع مشابه
Inf-sup Stable Nonconforming Finite Elements of Higher Order on Quadrilaterals and Hexahedra
Abstract. We present families of scalar nonconforming finite elements of arbitrary order r ≥ 1 with optimal approximation properties on quadrilaterals and hexahedra. Their vector-valued versions together with a discontinuous pressure approximation of order r − 1 form inf-sup stable finite element pairs of order r for the Stokes problem. The well-known elements by Rannacher and Turek are recover...
متن کاملAcute Triangulations of Doubly Covered Convex Quadrilaterals
Motivated by various applications triangulations of surfaces using only acute triangles have been recently studied. Triangles and quadrilaterals can be triangulated with at most 7, respectively 10, acute triangles. Doubly covered triangles can be triangulated with at most 12 acute triangles. In this paper we investigate the acute triangulations of doubly covered convex quadrilaterals, and show ...
متن کاملNonconforming elements in least-squares mixed finite element methods
In this paper we analyze the finite element discretization for the first-order system least squares mixed model for the second-order elliptic problem by means of using nonconforming and conforming elements to approximate displacement and stress, respectively. Moreover, on arbitrary regular quadrilaterals, we propose new variants of both the rotated Q1 nonconforming element and the lowest-order ...
متن کاملMerging the Bramble-Pasciak-Steinbach and the Crouzeix-Thomée criterion for H1-stability of the L2-projection onto finite element spaces
Suppose S ⊂ H1(Ω) is a finite-dimensional linear space based on a triangulation T of a domain Ω, and let Π : L2(Ω) → L2(Ω) denote the L2-projection onto S. Provided the mass matrix of each element T ∈ T and the surrounding mesh-sizes obey the inequalities due to Bramble, Pasciak, and Steinbach or that neighboring element-sizes obey the global growth-condition due to Crouzeix and Thomée, Π is H1...
متن کاملMerging the Bramble-pasciak-steinbach and the Crouzeix-thomée Criterion for H-stability of the L-projection onto Finite Element Spaces
Suppose S ⊂ H1(Ω) is a finite-dimensional linear space based on a triangulation T of a domain Ω, and let Π : L2(Ω) → L2(Ω) denote the L2-projection onto S. Provided the mass matrix of each element T ∈ T and the surrounding mesh-sizes obey the inequalities due to Bramble, Pasciak, and Steinbach or that neighboring element-sizes obey the global growth-condition due to Crouzeix and Thomée, Π is H1...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Numerical Analysis
دوره 50 شماره
صفحات -
تاریخ انتشار 2012