A Finite Element formulation of Simplicial General Relativity
نویسنده
چکیده
We will present a set of equations for General Relativity adapted to weak simplicial spacetimes. The equations will be obtained via a weak formulation of the field equations similar to the methods commonly used in finite element schemes. The equations will be shown to be a weighted sum of the Regge equations.
منابع مشابه
A left-handed simplicial action for euclidean general relativity
An action for simplicial euclidean general relativity involving only left-handed fields is presented. The simplicial theory is shown to converge to continuum general relativity in the Plebanski formulation as the simplicial complex is refined. This contrasts with the Regge model for which M. Miller and Brewin have shown that the full field equations are much more restrictive than Einstein’s in ...
متن کاملAxisymmetric Scaled Boundary Finite Element Formulation for Wave Propagation in Unbounded Layered Media
Wave propagation in unbounded layered media with a new formulation of Axisymmetric Scaled Boundary Finite Element Method (AXI-SBFEM) is derived. Dividing the general three-dimensional unbounded domain into a number of independent two-dimensional ones, the problem could be solved by a significant reduction in required storage and computational time. The equations of the corresponding Axisymmetri...
متن کاملExplicit Stiffness of Tapered and Monosymmetric i Beam-Columns
A formulation for finite element analysis of tapered and monosymmetric I shaped beam-columns is presented. This is a general way to analyze these types of complex elements. Based upon the formulation, member stiffness matrix is obtained explicitly. The element considered has seven nodal degrees of freedom. In addition, the related stability matrix is found. Numerical studies of the aforementio...
متن کاملFrom the Hu-washizu Formulation to the Average Nodal Strain Formulation
We present a stabilized finite element method for the Hu-Washizu formulation of linear elasticity based on simplicial meshes leading to the stabilized nodal strain formulation or node-based uniform strain elements. We show that the finite element approximation converges uniformly to the exact solution for the nearly incompressible case.
متن کاملA New Finite Element Formulation for Buckling and Free Vibration Analysis of Timoshenko Beams on Variable Elastic Foundation
In this study, the buckling and free vibration of Timoshenko beams resting on variable elastic foundation analyzed by means of a new finite element formulation. The Winkler model has been applied for elastic foundation. A two-node element with four degrees of freedom is suggested for finite element formulation. Displacement and rotational fields are approximated by cubic and quadratic polynomia...
متن کامل