Related papers: Consistent and mimetic discretizations in general …
We apply the ``consistent discretization'' approach to general relativity leaving the spatial slices continuous. The resulting theory is free of the diffeomorphism and Hamiltonian constraints, but one can impose the diffeomorphism…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum mechanics problems so that any property of the continuum that is proved using vector calculus can be proven in an analogous way…
We discuss in detail the uniform discretization approach to the quantization of totally constrained theories. This approach allows to construct the continuum theory of interest as a well defined, controlled, limit of well behaved discrete…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
We apply the ``consistent discretization'' technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions. The result is a well defined canonical theory that is free of constraints and…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…
Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…
This paper considers a large class of linear operator equations, including linear boundary value problems for partial differential equations, and treats them as linear recovery problems for objects from their data. Well-posedness of the…
We apply the consistent discretization scheme to general relativity particularized to the Gowdy space-times. This is the first time the framework has been applied in detail in a non-linear generally-covariant gravitational situation with…
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. Additionally, the traditional lattice field theory approach consists…
We consider time discretization methods for abstract parabolic problems with inhomogeneous linear constraints. Prototype examples that fit into the general framework are the heat equation with inhomogeneous (time dependent) Dirichlet…
A temporally varying discretization often features in discrete gravitational systems and appears in lattice field theory models subject to a coarse graining or refining dynamics. To better understand such discretization changing dynamics in…
An abstract framework is developed that enables the analysis of algebraically stabilized discretizations in a unified way. This framework is applied to a discretization of this kind for convection-diffusion-reaction equations. The…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong…