Related papers: A genuinely stable Lagrange-Galerkin scheme for co…
In this paper, we focus on designing a well-conditioned Glarkin spectral methods for solving a two-sided fractional diffusion equations with drift, in which the fractional operators are defined neither in Riemann-Liouville nor Caputo sense,…
We propose a numerical method for convection-diffusion problems under low regularity assumptions. We derive the method and analyze it using the primal-dual weak Galerkin (PDWG) finite element framework. The Euler-Lagrange formulation…
Spline Galerkin approximation methods for the Sherman-Lauricella integral equation on simple closed piecewise smooth contours are studied, and necessary and sufficient conditions for their stability are obtained. It is shown that the method…
In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear…
A direct discontinuous Galerkin (DDG) finite element method is developed for solving fractional convection-diffusion and Schr\"{o}dinger type equations with a fractional Laplacian operator of order $\alpha$ $(1<\alpha<2)$. The fractional…
In this study, we consider the simulation of subsurface flow and solute transport processes in the stationary limit. In the convection-dominant case, the numerical solution of the transport problem may exhibit non-physical diffusion and…
We consider an advection-diffusion equation that is both non-coercive and advection-dominated. We present a possible numerical approach, to our best knowledge new, and based on the invariant measure associated to the original equation. The…
We develop a cut Discontinuous Galerkin method (cutDGM) for a diffusion-reaction equation in a bulk domain which is coupled to a corresponding equation on the boundary of the bulk domain. The bulk domain is embedded into a structured,…
We propose a new integer programming formulation for the problem of finding a maximum stable set of a graph based on representatives of stable sets. In addition, we investigate exact solutions provided by a Lagrangian decomposition of this…
We present and analyze a discontinuous Galerkin method for the numerical modeling of a Kelvin-Voigt thermo/poro-viscoelastic problem. We present the derivation of the model and we develop a stability analysis in the continuous setting that…
We prove stability estimates for the spatially discrete, Galerkin solution of a fractional Fokker-Planck equation, improving on previous results in several respects. Our main goal is to establish that the stability constants are bounded…
In this paper, we develop a sparse grid discontinuous Galerkin (DG) scheme for transport equations and applied it to kinetic simulations. The method uses the weak formulations of traditional Runge-Kutta DG (RKDG) schemes for hyperbolic…
We introduce an automatic variationally stable analysis (AVS) for finite element (FE) computations of scalar-valued convection-diffusion equations with non-constant and highly oscillatory coefficients. In the spirit of least squares FE…
This work provides reliable a posteriori error estimates for Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems. The classes of systems we study are quite general with a focus on convection-dominated…
In this paper, we present a new variational integrator for problems in Lagrangian mechanics. Using techniques from Galerkin variational integrators, we construct a scheme for numerical integration that converges geometrically, and is…
We present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare the standard Galerkin discretization using the linear…
We present and analyze a structure-preserving method for the approximation of solutions to nonlinear cross-diffusion systems, which combines a Local Discontinuous Galerkin spatial discretization with the backward Euler time-stepping scheme.…
We present unconditionally energy stable Runge-Kutta (RK) discontinuous Galerkin (DG) schemes for solving a class of fourth order gradient flows. Our algorithm is geared toward arbitrarily high order approximations in both space and time,…
We present and analyze an unconditionally energy stable and convergent finite difference scheme for the Functionalized Cahn-Hilliard equation. One key difficulty associated with the energy stability is based on the fact that one nonlinear…
This paper presents a first-order convex splitting hybridizable/embedded discontinuous Galerkin method for the phase field crystal equation written in mixed form. Since the sixth-order phase field crystal equation is rewritten as a…