Mass-conservative and positivity preserving second-order semi-implicit methods for high-order parabolic equations

10/22/2020
by   Sana Keita, et al.
0

We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. In our approach, we first solve a variational problem and then an optimization problem to satisfy the desired physical properties of the solution such as conservation of mass, positivity (non-negativity) of solution and dissipation of energy. Furthermore, we show existence and uniqueness of the solution to the optimization problem and we prove that the methods converge to the truncation schemes <cit.>. We also propose new conservative truncation methods for high-order parabolic equations. A numerical convergence study is performed and a series of numerical tests are presented to show and compare the efficiency and robustness of the different schemes.

READ FULL TEXT

page 19

page 28

research
11/10/2019

A High order Conservative Flux Optimization Finite Element Method for Diffusion Equations

This article presents a high order conservative flux optimization (CFO) ...
research
07/26/2020

Conservative semi-Lagrangian schemes for kinetic equations Part I: Reconstruction

In this paper, we propose and analyse a reconstruction technique which e...
research
06/29/2021

Semi-implicit methods for advection equations with explicit forms of numerical solution

We present a parametric family of semi-implicit second order accurate nu...
research
07/21/2023

A high-order finite volume method for Maxwell's equations in heterogeneous and time-varying media

We develop a finite volume method for Maxwell's equations in materials w...
research
09/26/2021

A new Lagrange multiplier approach for constructing structure-preserving schemes, II. bound preserving

In the second part of this series, we use the Lagrange multiplier approa...

Please sign up or login with your details

Forgot password? Click here to reset