Optimal Convergence for Time-Dependent Stokes Equation: A New Approach

2021 ◽  
Vol 89 (3) ◽  
Author(s):  
D. Fishelov ◽  
J.-P. Croisille
Keyword(s):  
Stokes Equation ◽  
Time Dependent ◽  
New Approach ◽  
Optimal Convergence

scholarly journals Ultraviolet spectra of star-forming galaxies with time-dependent dust obscuration

2003 ◽  
Vol 212 ◽  
pp. 734-735
Author(s):  
Lucimara P. Martins ◽  
Claus Leitherer ◽  
Daniela Calzetti
Keyword(s):  
Stellar Wind ◽  
Time Dependent ◽  
New Technique ◽  
New Approach ◽  
Star Forming ◽  
Ultraviolet Spectra

We present a new approach to probe the properties of the most massive, ionizing stars with respect to the less massive, non-ionizing stars. The new technique utilizes stellar-wind lines, instead of the previously employed nebular lines. This allows us to probe the timescale of the dust dispersal in a very young obscured starburst from purely stellar diagnostics.

scholarly journals Discontinuous Galerkin time discretization methods for parabolic problems with linear constraints

2019 ◽  
Vol 27 (3) ◽  
pp. 155-182 ◽  
Author(s):  
Igor Voulis ◽  
Arnold Reusken
Keyword(s):  
Discontinuous Galerkin ◽  
Error Bounds ◽  
Convergence Rates ◽  
Time Discretization ◽  
Linear Constraints ◽  
Dirichlet Boundary Conditions ◽  
Time Dependent ◽  
Parabolic Problems ◽  
Discretization Methods ◽  
Optimal Convergence

Abstract 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 boundary conditions and the time-dependent Stokes equation with an inhomogeneous divergence constraint. Two common ways of treating such linear constraints, namely explicit or implicit (via Lagrange multipliers) are studied. These different treatments lead to different variational formulations of the parabolic problem. For these formulations we introduce a modification of the standard discontinuous Galerkin (DG) time discretization method in which an appropriate projection is used in the discretization of the constraint. For these discretizations (optimal) error bounds, including superconvergence results, are derived. Discretization error bounds for the Lagrange multiplier are presented. Results of experiments confirm the theoretically predicted optimal convergence rates and show that without the modification the (standard) DG method has sub-optimal convergence behavior.

scholarly journals On a direct method for the determination of an exact invariant for the time-dependent harmonic oscillator

1977 ◽  
Vol 20 (1) ◽  
pp. 97-105 ◽  
Author(s):  
P. G. L. Leach
Keyword(s):  
Direct Method ◽  
Dynamical Symmetry ◽  
Time Dependent ◽  
Symmetry Groups ◽  
New Approach ◽  
One Dimensional ◽  
The One ◽  
A Direct Method ◽  
Exact Invariant

AbstractAn exact invariant is found for the one-dimensional oscillator with equation of motion . The method used is that of linear canonical transformations with time-dependent coeffcients. This is a new approach to the problem and has the advantage of simplicity. When f(t) and g(t) are zero, the invariant is related to the well-known Lewis invariant. The significance of extension to higher dimension of these results is indicated, in particular for the existence of non-invariance dynamical symmetry groups.

scholarly journals Two-Way Coupling Fluid-Structure Interaction (FSI) Approach to Inertial Focusing Dynamics Under Dean Flow Patterns in Asymmetric Serpentines

2018 ◽  
Author(s):  
Eric Pedrol ◽  
Jaume Massons ◽  
Francesc Díaz ◽  
Magdalena Aguiló
Keyword(s):  
Finite Element Method ◽  
Secondary Flow ◽  
Stokes Flow ◽  
Time Dependent ◽  
Local Flow ◽  
New Approach ◽  
Fem Simulations ◽  
Inertial Focusing ◽  
Dean Flow ◽  
Structure Interaction

The dynamics of a spherical particle in an asymmetric serpentine is studied by finite element method (FEM) simulations in a physically unconstrained system. The two-way coupled time dependent solutions illustrate the path of the particle along a curve where a secondary flow (Dean flow) has developed. The simulated conditions were adjusted to match those of an experiment for which particles were focused under inertial focusing conditions. The obtained rotational modes allowed to infer the influence of the local flow around the particle. We propose a new approach to find the decoupled secondary flow contribution employing a quasi-Stokes flow.

scholarly journals Two-Way Coupling FSI Approach to Inertial Focusing Dynamics Under Dean Flow Patterns in Asymmetric Serpentines

2018 ◽  
Author(s):  
Eric Pedrol ◽  
Jaume Massons ◽  
Francesc Díaz ◽  
Magdalena Aguiló
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Secondary Flow ◽  
Stokes Flow ◽  
Time Dependent ◽  
Local Flow ◽  
New Approach ◽  
Fem Simulations ◽  
Inertial Focusing ◽  
Dean Flow

The dynamics of a spherical particle in an asymmetric serpentine is studied by finite element method (FEM) simulations in a physically unconstrained system. The two-way coupled time dependent solutions illustrate the path of the particle along a curve where a secondary flow (Dean flow) has developed. The simulated conditions were adjusted to match those of an experiment for which particles were focused under inertial focusing conditions. The obtained rotational modes allowed to infer the influence of the local flow around the particle. We propose a new approach to find the decoupled secondary flow contribution employing a quasi-Stokes flow.

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