Fully implicit local time-stepping methods for advection-diffusion problems in mixed formulations

10/03/2021
by   Thi-Thao-Phuong Hoang, et al.
0

This paper is concerned with numerical solution of transport problems in heterogeneous porous media. A semi-discrete continuous-in-time formulation of the linear advection-diffusion equation is obtained by using a mixed hybrid finite element method, in which the flux variable represents both the advective and diffusive flux, and the Lagrange multiplier arising from the hybridization is used for the discretization of the advective term. Based on global-in-time and nonoverlapping domain decomposition, we propose two implicit local time-stepping methods to solve the semi-discrete problem. The first method uses the time-dependent Steklov-Poincaré type operator and the second uses the optimized Schwarz waveform relaxation (OSWR) with Robin transmission conditions. For each method, we formulate a space-time interface problem which is solved iteratively. Each iteration involves solving the subdomain problems independently and globally in time; thus, different time steps can be used in the subdomains. The convergence of the fully discrete OSWR algorithm with nonmatching time grids is proved. Numerical results for problems with various Peclét numbers and discontinuous coefficients, including a prototype for the simulation of the underground storage of nuclear waste, are presented to illustrate the performance of the proposed local time-stepping methods.

READ FULL TEXT

page 25

page 26

page 28

10/03/2021

Optimized Ventcel-Schwarz waveform relaxation and mixed hybrid finite element method for transport problems

This paper is concerned with the optimized Schwarz waveform relaxation m...
10/05/2021

A space-time multiscale mortar mixed finite element method for parabolic equations

We develop a space-time mortar mixed finite element method for parabolic...
02/12/2022

Fast and accurate domain decomposition methods for reduced fracture models with nonconforming time grids

This paper is concerned with the numerical solution of compressible flui...
07/03/2020

A global-in-time domain decomposition method for the coupled nonlinear Stokes and Darcy flows

We study a decoupling iterative algorithm based on domain decomposition ...
02/04/2022

Convergence Analysis of Virtual Element Method for Nonlinear Nonlocal Dynamic Plate Equation

In this article, we have considered a nonlinear nonlocal time dependent ...
04/07/2022

A unified theory of non-overlapping Robin-Schwarz methods – continuous and discrete, including cross points

Non-overlapping Schwarz methods with generalized Robin transmission cond...
03/04/2021

An FFT framework for simulating non-local ductile failure in heterogeneous materials

The simulation of fracture using continuum ductile damage models attains...