Stable Spectral Methods on Tetrahedral Elements
نویسندگان
چکیده
منابع مشابه
Stable Spectral Methods on Tetrahedral Elements
A framework for the construction of stable spectral methods on arbitrary domains with unstructured grids is presented. Although most of the developments are of a general nature, an emphasis is placed on schemes for the solution of partial differential equations defined on the tetrahedron. In the first part the question of well-behaved multivariate polynomial interpolation on the tetrahedron is ...
متن کاملTriangular and tetrahedral spectral elements
In this paper we present a new unstructured spectral element method for use on triangular and tetrahedral subdomains. The algorithm maintains the accuracy and efficiency of standard quadrilateral/hexahedral spectral element methods but offers greater adaptivity. Standard unstructured meshes can be used and the order of the polynomial expansion can be varied within each triangular/tetrahedral su...
متن کاملDivergence-free finite elements on tetrahedral grids for k≥6
It was shown two decades ago that the Pk-Pk−1 mixed element on triangular grids, approximating the velocity by the continuous Pk piecewise polynomials and the pressure by the discontinuous Pk−1 piecewise polynomials, is stable for all k ≥ 4, provided the grids are free of a nearly-singular vertex. The problem with the method in 3D was posted then and remains open. The problem is solved partiall...
متن کاملNonconforming Tetrahedral Mixed Finite Elements for Elasticity
This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear vector fields for displacement, this gives a stable mixed finite element method which is shown to be linearly convergent for both the stress and displacement, an...
متن کاملTetrahedral and hexahedral invertible finite elements
We review an algorithm for the finite element simulation of elastoplastic solids which is capable of robustly and efficiently handling arbitrarily large deformation. In fact, the model remains valid even when large parts of the mesh are inverted. The algorithm is straightforward to implement and can be used with any material constitutive model, and for both volumetric solids and thin shells suc...
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: SIAM Journal on Scientific Computing
سال: 2000
ISSN: 1064-8275,1095-7197
DOI: 10.1137/s1064827598343723