A fully discrete penalty finite element method is presented for the two-dimensional time-dependent Navier-Stokes equations. The time discretization of the penalty Navier-Stokes equations is based on the backward Euler scheme; the spatial discretization of the time discretized penalty Navier-Stokes equations is based on a finite element space pair (Xh,Mh) which satisfies some approximate assumpt...

This paper presents a class of parallel numerical integration methods for stii systems of ordinary diierential equations which can be partitioned into loosely coupled subsystems. The formulas are called decoupled backward diierentiation formulas, and they are derived from the classical formulas by restricting the implicit part to the diagonal subsystem. With one or several subsystems allocated ...

We develop and analyze methods based on combining the lowest-order mixed finite element method with backward Euler time discretization for the solution of diffusion problems on dynamically changing meshes. The methods developed are shown to preserve the optimal rate error estimates that are well known for static meshes. The novel aspect of the scheme is the construction of a linear approximatio...

This is a continuation of the first author’s earlier paper [17] jointly with Pang and Deng, in which the authors established some sufficient conditions under which the Euler–Maruyama (EM) method can reproduce the almost sure exponential stability of the test hybrid SDEs. The key condition imposed in [17] is the global Lipschitz condition. However, we will show in this paper that without this gl...

In this paper, we consider the cascadic multigrid method for a parabolic type equation. Backward Euler approximation in time and linear finite element approximation in space are employed. A stability result is established under some conditions on the smoother. Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter, t...

In this paper, a nonconforming mixed finite element method (FEM) is presented to approximate time-dependent Maxwell’s equations in a three-dimensional bounded domain with absorbing boundary conditions (ABC). By employing traditional variational formula, instead of adding penalty terms, we show that the discrete scheme is robust. Meanwhile, with the help of the element’s typical properties and d...

The paper is concerned with a scalar conservation law with nonlocal flux, providing a model for granular flow with slow erosion and deposition. While the solution u = u(t, x) can have jumps, the inverse function x = x(t, u) is always Lipschitz continuous; its derivative has bounded variation and satisfies a balance law with measure-valued sources. Using a backward Euler approximation scheme com...

We analyze the spatially semidiscrete piecewise linear finite element method for a nonlocal parabolic equation resulting from thermistor problem. Our approach is based on the properties of the elliptic projection defined by the bilinear form associated with the variational formulation of the finite element method. We assume minimal regularity of the exact solution that yields optimal order erro...

We study a natural Wasserstein gradient flow on manifolds of probability distributions with discrete sample spaces. We derive the Riemannian structure for the probability simplex from the dynamical formulation of the Wasserstein distance on a weighted graph. We pull back the geometric structure to the parameter space of any given probability model, which allows us to define a natural gradient f...

In this paper, a multi-point flux mixed-finite-element decoupled method was considered for the compressible miscible displacement problem. For problem, fully discrete backward Euler scheme proposed, in which velocity and pressure equations were by MFE using BDM1 elements combined with trapezoidal quadrature rule. The concentration equation handled standard FE method. error analysis velocity, pr...