Related papers: Second order in time finite element schemes for cu…
We consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The scheme for the curve evolution…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
In this paper, a semi-discrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fractional derivative of order $\alpha \in (0,1)$ in a…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
This paper contributes to the exploration of a recently introduced computational paradigm known as second-order flows, which are characterized by novel dissipative hyperbolic partial differential equations extending accelerated gradient…
This paper is concerned with the application of finite element methods to obtain solutions for steady fully developed second-grade flows in a curved pipe of circular cross-section and arbitrary curvature ratio, under a given axial pressure…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
We consider an implicit finite difference scheme on uniform grids in time and space for the Cauchy problem for a second order parabolic stochastic partial differential equation where the parabolicity condition is allowed to degenerate. Such…
Two-fluid relativistic plasma flow equations combine the equations of relativistic hydrodynamics with Maxwell's equations for electromagnetic fields, which involve divergence constraints for the magnetic and electric fields. When developing…
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
A space-discretization for the elastic flow of inextensible curves is devised and quasi-optimal convergence of the corresponding semi-discrete problem is proved for a suitable discretization of the nonlinear inextensibility constraint.…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman equations in the context of stochastic optimal control, or…
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…
A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded…
We consider the initial/boundary value problem for the fractional diffusion and diffusion-wave equations involving a Caputo fractional derivative in time. We develop two "simple" fully discrete schemes based on the Galerkin finite element…
In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase…
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…