The Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability restriction when using an explicit time discretization. In this paper, we propose several efficient semiimplicit schemes to remove this stiffness from the Immer...

This paper studies the convergence of three temporal semi-discretizations for a backward semilinear stochastic evolution equation. For general terminal value and coefficient with Lipschitz continuity, first two is established, an explicit rate derived third semi-discretization. The semi-discretization applied to linear quadratic control problem, temporally semi-discrete approximation optimal es...

Data discretization is needed for various reasons. One reason is that there are many machine learning algorithms that can only be applied to discrete data. In order to use those algorithms, we need to discretize the data. We might also want to do that for solely computational reasons; some problems are easier to compute for discrete variables. Finally, if we know that our data is discrete, but ...

We establish sharp energy decay rates for a large class of nonlinearly first-order damped systems, and we design discretization schemes that inherit of the same energy decay rates, uniformly with respect to the space and/or time discretization parameters, by adding appropriate numerical viscosity terms. Our main arguments use the optimal-weight convexity method and uniform observability inequal...