Related papers: Arbitrary high-order unconditionally stable method…
This paper presents a high-order accurate Continuous Galerkin Finite Element Method (CGFEM) for solving the initial boundary value problems governed by the Incompressible Navier-Stokes (INS) equations. We discretize the INS equations using…
This work is concerned with the uniform accuracy of implicit-explicit backward differentiation formulas for general linear hyperbolic relaxation systems satisfying the structural stability condition proposed previously by the third author.…
An adaptive implicit-explicit (IMEX) BDF2 scheme is investigated on generalized SAV approach for the Cahn-Hilliard equation by combining with Fourier spectral method in space. It is proved that the modified energy dissipation law is…
In this work, we have discretized a system of time-dependent nonlinear convection-diffusion-reaction equations with the virtual element method over the spatial domain and the Euler method for the temporal interval. For the nonlinear…
For linear transport and radiative heat transfer equations with random inputs, we develop new generalized polynomial chaos based Asymptotic-Preserving stochastic Galerkin schemes that allow efficient computation for the problems that…
The analysis of a delayed generalized Burgers-Huxley equation (a non-linear advection-diffusion-reaction problem) with weakly singular kernels is carried out in this work. Moreover, numerical approximations are performed using the…
Linear stationary reaction-convection-diffusion equations with Dirichlet boundary conditions are approximated using a simple finite difference method corresponding to central differences and the addition of a high-order stabilization term…
We consider a system of two singularly perturbed Boundary Value Problems (BVPs) of convection-diffusion type with discontinuous source terms and a small positive parameter multiplying the highest derivatives. Then their solutions exhibit…
We consider the initial boundary value problem for the homogeneous time-fractional diffusion equation $\partial^\alpha_t u - \De u =0$ ($0< \alpha < 1$) with initial condition $u(x,0)=v(x)$ and a homogeneous Dirichlet boundary condition in…
The immersed boundary-finite element method (IBFE) is an approach to describing the dynamics of an elastic structure immersed in an incompressible viscous fluid. In this formulation, there are discontinuities in the pressure and viscous…
A new class of implicit-explicit (IMEX) methods combined with a p-adaptive mixed finite element formulation is proposed to simulate the diffusion of reacting species. Hierarchical polynomial functions are used to construct an…
The goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak…
We develop a family of stabilized backward differentiation formula (sBDF) schemes of orders one through four for semilinear parabolic equations. The proposed methods are designed to achieve three properties that are rarely available…
In this paper we propose and analyze an interior penalty discontinuous Galerkin (IP-DG) method using piecewise linear polynomials for the elastic Helmholtz equations with the first order absorbing boundary condition. It is proved that the…
We consider the initial boundary value problem for the inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and a nonsmooth right hand side data in a bounded convex polyhedral domain. We analyze…
This paper analyses discontinuous Galerkin finite element methods (DGFEM) to approximate a regular solution to the von K\'arm\'an equations defined on a polygonal domain. A discrete inf-sup condition sufficient for the stability of the…
We formulate the immersed-boundary method (IBM) as an inverse problem. A control variable is introduced on the boundary of a larger domain that encompasses the target domain. The optimal control is the one that minimizes the mismatch…
This paper is concerned about the implicit-explicit (IMEX) methods for a class of dissipative wave systems with time-varying velocity feedbacks and nonlinear potential energies, equipped with different boundary conditions. Firstly, we…
In this note we consider the continuous Galerkin time stepping method of arbitrary order as a possible discretization scheme of nonlinear initial value problems. In addition, we develop and generalize a well known existing result for the…
This paper is concerned with initial-boundary-value problems (IBVPs) for a class of nonlinear Schr\"odinger equations posed either on a half line $\mathbb{R}^+$ or on a bounded interval $(0, L)$ with nonhomogeneous boundary conditions. For…