We consider the Stokes problem on a plane polygonal domain Ω ⊂ 2. We propose a finite element method for overlapping or nonmatching grids for the Stokes problem based on the partition of unity method. We prove that t...
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There have been extensive studies on the large time behavior of solutions to systems on gas motions, such as the Navier-Stokes equations and the Boltzmann equation. Recently, an approach is introduced by combining the...
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There have been extensive studies on the large time behavior of solutions to systems on gas motions, such as the Navier-Stokes equations and the Boltzmann equation. Recently, an approach is introduced by combining the energy method and the spectral analysis to the study of the optimal rates of convergence to the asymptotic profiles. In this paper, we will first illustrate this method by using some simple model and then we will present some recent results on the Navier-Stokes equations and the Boltzmann equation. Precisely, we prove the stability of the non-trivial steady state for the Navier-Stokes equations with potential forces and also obtain the optimal rate of convergence of solutions toward the steady state. The same issue was also studied for the Boltzmann equation in the presence of the general time-space dependent forces. It is expected that this approach can also be applied to other dissipative systems in fluid dynamics and kinetic models such as the model system of radiating gas and the Vlasov-Poisson-Boltzmann system.
Numerous C^0 discontinuous Galerkin (DG) schemes for the Kirchhoff plate bending problem are extended to solve a plate frictional contact problem, which is a fourth-order elliptic variational inequality of the second ...
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Numerous C^0 discontinuous Galerkin (DG) schemes for the Kirchhoff plate bending problem are extended to solve a plate frictional contact problem, which is a fourth-order elliptic variational inequality of the second kind. This variational inequality contains a nondifferentiable term due to the frictional contact. We prove that these C^0 DG methods are consis tent and st able, and derive optimal order error estima tes for the quadratic element. A numerical example is presented to show the performance of the C^0 DG methods;and the numerical convergence orders confirm the theoretical prediction.
Exact solutions to the shallow wave equation are studied based on the idea of the extended homoclinic test and bilinear method. Some explicit solutions, such as the one soliton solution, the doubly-periodic wave solut...
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Exact solutions to the shallow wave equation are studied based on the idea of the extended homoclinic test and bilinear method. Some explicit solutions, such as the one soliton solution, the doubly-periodic wave solution and the periodic solitary wave solutions, are obtained. In addition, the properties of the solutions are investigated.
The radiative transfer equation (RTE) arises in a variety of applications. The equation is challenging to solve numerically for a couple of reasons: high dimensionality, integro-differential form, highly forward-peake...
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In earlier papers, 2π-periodic spectral data windows have been used in spectral estimation of discrete-time random fields having finite second-order moments. In this paper, we show that 2π-periodic spectral windows ...
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In earlier papers, 2π-periodic spectral data windows have been used in spectral estimation of discrete-time random fields having finite second-order moments. In this paper, we show that 2π-periodic spectral windows can also be used to construct estimates of the spectral density of a homoge-neous symmetric α-stable discrete-time random field. These fields do not have second-order moments if 0 < α < 2. We construct an estimate of the spectrum, calculate the asymptotic mean and variance, and prove weak consistency of our estimate.
The Onsager-Machlup(OM)functional is well known for characterizing the most probable transition path of a diffusion process with non-vanishing ***,it suffers from a notorious issue that the functional is unbounded bel...
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The Onsager-Machlup(OM)functional is well known for characterizing the most probable transition path of a diffusion process with non-vanishing ***,it suffers from a notorious issue that the functional is unbounded below when the specified transition time T goes to *** hinders the interpretation of the results obtained by minimizing the OM *** provide a new perspective on this *** mild conditions,we show that although the infimum of the OM functional becomes unbounded when T goes to infinity,the sequence of minimizers does contain convergent subsequences on the space of *** graph limit of this minimizing subsequence is an extremal of the abbreviated action functional,which is related to the OM functional via the Maupertuis principle with an optimal *** further propose an energy-climbing geometric minimization algorithm(EGMA)which identifies the optimal energy and the graph limit of the transition path *** algorithm is successfully applied to several typical examples in rare event *** interesting comparisons with the Freidlin-Wentzell action functional are also made.
The impact of topological terms that modify the Hilbert-Einstein action is here explored by virtue of a further f(G) contribution. In particular, we investigate the phase-space stability and critical points of an equi...
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In this article, we construct a two-dimensional model for the nonlinearly elastic flexural shell using differential geometry and tensor analysis under the assumption that flexural energy is dominant, that is, the metr...
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A partial Runge-Kutta Discontinuous Galerkin(RKDG)method which preserves the exactly divergence-free property of the magnetic field is proposed in this paper to solve the two-dimensional ideal compressible magnetohydr...
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A partial Runge-Kutta Discontinuous Galerkin(RKDG)method which preserves the exactly divergence-free property of the magnetic field is proposed in this paper to solve the two-dimensional ideal compressible magnetohydrodynamics(MHD)equations written in semi-Lagrangian formulation on moving quadrilateral *** this method,the fluid part of the ideal MHD equations along with zcomponent of the magnetic induction equation is discretized by the RKDG method as our previous paper[47].The numerical magnetic field in the remaining two directions(i.e.,x and y)are constructed by using the magnetic flux-freezing principle which is the integral form of the magnetic induction equation of the ideal *** the divergence of the magnetic field in 2D is independent of its z-direction component,an exactly divergence-free numerical magnetic field can be obtained by this *** propose a new nodal solver to improve the calculation accuracy of velocities of the moving meshes.A limiter is presented for the numerical solution of the fluid part of the MHD equations and it can avoid calculating the complex eigen-system of the MHD *** numerical examples are presented to demonstrate the accuracy,non-oscillatory property and preservation of the exactly divergence-free property of our method.
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