DeepAI AI Chat
Log In Sign Up

Continuous data assimilation and long-time accuracy in a C^0 interior penalty method for the Cahn-Hilliard equation

by   Amanda E. Diegel, et al.

We propose a numerical approximation method for the Cahn-Hilliard equations that incorporates continuous data assimilation in order to achieve long time accuracy. The method uses a C^0 interior penalty spatial discretization of the fourth order Cahn-Hilliard equations, together with a backward Euler temporal discretization. We prove the method is long time stable and long time accurate, for arbitrarily inaccurate initial conditions, provided enough data measurements are incorporated into the simulation. Numerical experiments illustrate the effectiveness of the method on a benchmark test problem.


Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations

We study a continuous data assimilation (CDA) algorithm for a velocity-v...

The BDF2-Maruyama Scheme for Stochastic Evolution Equations with Monotone Drift

We study the numerical approximation of stochastic evolution equations w...

Numerical analysis of an efficient second order time filtered backward Euler method for MHD equations

The present work is devoted to introduce the backward Euler based modula...

A note on the accuracy of the generalized-α scheme for the incompressible Navier-Stokes equations

We investigate the temporal accuracy of two generalized-α schemes for th...

Continuous Data Assimilation for the Double-Diffusive Natural Convection

In this study, we analyzed a continuous data assimilation scheme applied...

Transforming Butterflies into Graphs: Statistics of Chaotic and Turbulent Systems

We formulate a data-driven method for constructing finite volume discret...

The order barrier for the L^1-approximation of the log-Heston SDE at a single point

We study the L^1-approximation of the log-Heston SDE at the terminal tim...