Related papers: Virtual element method for the system of time depe…
We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element…
This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe's method. We use the implicit Euler scheme for the time discretization. Consequently, in each step, an…
We establish the existence theory of several commonly used finite element (FE) nonlinear fully discrete solutions, and the convergence theory of a linearized iteration. First, it is shown for standard FE, SUPG and edge-averaged method…
This paper introduces a novel approach to approximate a broad range of reaction-convection-diffusion equations using conforming finite element methods while providing a discrete solution respecting the physical bounds given by the…
This article presents a priori error estimates of the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the $H(\rm div)$ conforming virtual element method (VEM) for the approximation of the…
This manuscript deals with the analysis of numerical methods for the full discretization (in time and space) of the linear heat equation with Neumann boundary conditions, and it provides the reader with error estimates that are uniform in…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
This article presents stability and convergence analyses of subgrid multiscale stabilized finite element formulation of non-Newtonian power-law fluid flow model strongly coupled with variable coefficients Advection-Diffusion-Reaction…
We analyze the convergence of an iterative method for solving the nonlinear system resulting from a natural discretization of the Monge-Amp\`ere equation with $C^1$ conforming approximations. We make the assumption, supported by numerical…
We consider numerical methods for linear parabolic equations in one spatial dimension having piecewise constant diffusion coefficients defined by a one parameter family of interface conditions at the discontinuity. We construct immersed…
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…
We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time…
In this paper, we propose a linearized finite element method (FEM) for solving the cubic nonlinear Schr\"{o}dinger equation with wave operator. In this method, a modified leap-frog scheme is applied for time discretization and a Galerkin…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…
We propose a fourth-order unfitted characteristic finite element method to solve the advection-diffusion equation on time-varying domains. Based on a characteristic-Galerkin formulation, our method combines the cubic MARS method for…
In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order $\alpha\in(3/2, 2)$ in the leading term and…
In this article, we present a numerical approach to ensure the preservation of physical bounds on the solutions to linear and nonlinear hyperbolic convection-reaction problems at the discrete level. We provide a rigorous framework for error…
We present a space-time virtual element method for the discretization of the heat equation, which is defined on general prismatic meshes and variable degrees of accuracy. Strategies to handle efficiently the space-time mesh structure are…
In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-reaction equation and two additional nonlinear ordinary…
We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on a monolithic convex limiting approach and prove a…