A nonconforming finite element method for fourth order curl equations in $\mathbb{R}^{3}$
نویسندگان
چکیده
منابع مشابه
A Nonconforming Finite Element Method for Fourth Order Curl Equations in R
In this paper we present a nonconforming finite element method for solving fourth order curl equations in three dimensions arising from magnetohydrodynamics models. We show that the method has an optimal error estimate for a model problem involving both (∇×)2 and (∇×)4 operators. The element has a very small number of degrees of freedom, and it imposes the inter-element continuity along the tan...
متن کاملA nonconforming finite element method for fourth order curl equations in R3
In this paper we present a nonconforming finite element method for solving fourth order curl equations in three dimensions arising from magnetohydrodynamics models. We show that the method has an optimal error estimate for a model problem involving both (∇×)2 and (∇×)4 operators. The element has a very small number of degrees of freedom, and it imposes the inter-element continuity along the tan...
متن کاملA nonconforming finite element method for a two-dimensional curl-curl and grad-div problem
Abstract. A numerical method for a two-dimensional curl-curl and grad-div problem is studied in this paper. It is based on a discretization using weakly continuous P1 vector fields and includes two consistency terms involving the jumps of the vector fields across element boundaries. Optimal convergence rates (up to an arbitrary positive ) in both the energy norm and the L2 norm are established ...
متن کاملNonconforming tetrahedral finite elements for fourth order elliptic equations
This paper is devoted to the construction of nonconforming finite elements for the discretization of fourth order elliptic partial differential operators in three spatial dimensions. The newly constructed elements include two nonconforming tetrahedral finite elements and one quasi-conforming tetrahedral element. These elements are proved to be convergent for a model biharmonic equation in three...
متن کاملNonconforming Mixed Finite Element Method for Nonlinear Hyperbolic Equations
A nonconforming mixed finite element method for nonlinear hyperbolic equations is discussed. Existence and uniqueness of the solution to the discrete problem are proved. Priori estimates of optimal order are derived for both the displacement and the stress.
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: Mathematics of Computation
سال: 2011
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2011-02480-4