We present a novel monolithic divergence-conforming HDG scheme for linear fluid-structure interaction problem with thick structure. A pressure-robust optimal energy-norm estimate is obtained the semidiscrete scheme. When combined Crank--Nicolson time discretization, our fully discrete energy stable and produces an exactly divergence-free fluid velocity approximation. The resulting system, which...

To study the heat or diffusion equation it is often used the Crank-Nicolson method which is unconditionally stable and has order of convergence O(k + h ), where k and h are mesh con2 2 stants. Unfortunately, using this method in conventional floatingpoint arithmetic we get solutions including not only the method error, but also representation and rounding error, Therefore, we propose an interva...

A linearized numerical scheme is proposed to solve the nonlinear time-fractional parabolic problems with time delay. The based on standard Galerkin finite element method in spatial direction, fractional Crank-Nicolson method, and extrapolation methods temporal direction. novel discrete Grönwall inequality established. Thanks inequality, error estimate of a fully obtained. Several examples are p...

It is shown that A-acceptable and, more generally, A()-acceptablerational approximations of bounded analytic semigroups in Banach space are stable. The result applies, in particular, to the Crank-Nicolson method.

Flow movement in unsaturated soil can be expressed by a partial differential equation, named Richards equation. The objective of this study is the finding of an appropriate implicit numerical solution for head based Richards equation. Some of the well known finite difference schemes (fully implicit, Crank Nicolson and Runge-Kutta) have been utilized in this study. In addition, the effects of di...

It is well accepted by physicists that the Manakov PMD equation is a good model to describe the evolution of nonlinear electric elds in optical bers with randomly varying birefringence. In the regime of the di usion approximation theory, an e ective asymptotic dynamics has recently been obtained to describe this evolution. This equation is called the stochastic Manakov equation. In this article...