Related papers: A Spectral Localization Method for Time-Fractional…
In this paper, we propose an accurate numerical means built upon a spectral-Galerkin method in spatial discretization and an enriched multi-step spectral-collocation approach in temporal direction, for Maxwell equations in Cole-Cole…
We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows.…
In this article, we addressed the numerical solution of a non-linear evolutionary variational inequality, which is encountered in the investigation of quasi-static contact problems. Our study encompasses both the semi-discrete and…
We present an algorithm for constructing numerical solutions to one--dimensional nonlinear, variable coefficient boundary value problems. This scheme is based upon applying the Homotopy Analysis Method (HAM) to decompose a nonlinear…
We study continuous finite element dicretizations for one dimensional hyperbolic partial differential equations. The main contribution of the paper is to provide a fully discrete spectral analysis, which is used to suggest optimal values of…
We evaluate the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations. The methods are based on affine combinations of time-splitting integrators and…
Simulation of unsteady creeping flows in complex geometries has traditionally required the use of a time-stepping procedure, which is typically costly and unscalable. To reduce the cost and allow for computations at much larger scales, we…
In this paper, we are concerned with the numerical solution for the backward fractional Feynman-Kac equation with non-smooth initial data. Here we first provide the regularity estimate of the solution. And then we use the backward Euler and…
In this paper, we develop a second-order accurate time-stepping scheme for the tempered time-fractional advection-dispersion equation based on a sum-of-exponentials (SOE) approximation to the convolution kernel involved in the fractional…
We investigate numerically a quasi-static elasticity system of Kachanov-type. To do so we propose an Euler time discretization combined with a suitable finite elements scheme (FEM) to handle the discretization is space. We use ODE-type…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
We consider the Shallow Water equations in the supercritical and subcritical cases in one space variable,posed in a finite spatial interval with characteristic boundary conditions at the endpoints, which, as is well known, are…
This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial…
In this paper we consider fully discrete approximations with inf-sup stable mixed finite element methods in space to approximate the Navier-Stokes equations. A continuous downscaling data assimilation algorithm is analyzed in which…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
We consider an initial/boundary value problem for one-dimensional fractional-order parabolic equations with a space fractional derivative of Riemann-Liouville type and order $\alpha\in (1,2)$. We study a spatial semidiscrete scheme with the…
Boundary element methods (BEM) reduce a partial differential equation in a domain to an integral equation on the domain's boundary. They are particularly attractive for solving problems on unbounded domains, but handling the dense matrices…
Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…
We analyse three time integration schemes for unfitted methods in fluid structure interaction. In Alghorithm 1 we propose a fully discrete monolithic algorithm with P1 P1 stabilized finite elements for the fluid problem; for this alghorithm…
Uncertainty quantification appears today as a crucial point in numerous branches of science and engineering. In the past two decades, a growing interest has been devoted to stochastic finite element method (SFEM) for the propagation of…