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A new simple Lagrangian method with favorable stability and efficiency properties for computing general plane curve evolutions is presented. The method is based on the flowing finite volume discretization of the intrinsic partial…
A high-accuracy time discretization is discussed to numerically solve the nonlinear fractional diffusion equation forced by a space-time white noise. The main purpose of this paper is to improve the temporal convergence rate by modifying…
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…
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 present a numerical study of the Einstein equations, according to the Arnowitt-Deser-Misner (ADM) formalism, in order to simulate the dynamics of gravitational fields. We took in consideration the original $3+1$ decomposition of the ADM…
This paper focusses on finite volume schemes for solving multilayer diffusion problems. We develop a finite volume method that addresses a deficiency of recently proposed finite volume/difference methods, which consider only a limited…
This study proposes a novel spatial discretization procedure for the compressible Euler equations that guarantees entropy conservation at a discrete level for thermally perfect gases. The procedure is based on a locally conservative…
We develop, and implement in a Finite Volume environment, a density-based approach for the Euler equations written in conservative form using density, momentum, and total energy as variables. Under simplifying assumptions, these equations…
In this paper, we introduce and analyze a class of numerical schemes that demonstrate remarkable superiority in terms of efficiency, the preservation of positivity, energy stability, and high-order precision to solve the time-dependent…
This paper detailedly discusses the locally one-dimensional numerical methods for efficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional…
We propose a new Eulerian-Lagrangian Runge-Kutta finite volume method for numerically solving convection and convection-diffusion equations. Eulerian-Lagrangian and semi-Lagrangian methods have grown in popularity mostly due to their…
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
This article studies a dirichlet boundary value problem for singularly perturbed time delay convection diffusion equation with degenerate coefficient. A priori explicit bounds are established on the solution and its derivatives. For…
A local discontinuous Galerkin (LDG) method for approximating large deformations of prestrained plates is introduced and tested on several insightful numerical examples in our previous computational work. This paper presents a numerical…
Explicit numerical finite difference schemes for partial differential equations are well known to be easy to implement but they are particularly problematic for solving equations whose solutions admit shocks, blowups and discontinuities.…
Numerical simulations of the air in the atmosphere and water in the oceans are essential for numerical weather prediction. The state-of-the-art for performing these fluid simulations relies on an Eulerian viewpoint, in which the fluid…
This article is concerned with the discretisation of the Stokes equations on time-dependent domains in an Eulerian coordinate framework. Our work can be seen as an extension of a recent paper by Lehrenfeld & Olshanskii [ESAIM: M2AN,…
We propose a novel class of temporal high-order parametric finite element methods for solving a wide range of geometric flows of curves and surfaces. By incorporating the backward differentiation formulae (BDF) for time discretization into…
We consider the simulation of barotropic flow of gas in long pipes and pipe networks. Based on a Hamiltonian reformulation of the governing system, a fully discrete approximation scheme is proposed using mixed finite elements in space and…
We present a natural framework for constructing energy-stable time discretization schemes. By leveraging the Onsager principle, we demonstrate its efficacy in formulating partial differential equation models for diverse gradient flow…