Abstract In this paper, a backward Euler method combined with finite element discretization in spatial direction is discussed for the equations of motion arising two-dimensional Oldroyd model viscoelastic fluids order one forcing term independent time or $L^{\infty }$ time. It shown that estimates discrete solution Dirichlet norm bounded uniformly Optimal priori error estimate $\textbf {L}^2$-n...

In this paper, we consider reinitializing level functions through equation /tþ sgnð/Þðkr/k 1Þ 1⁄4 0 [16]. The method of Russo and Smereka [11] is taken in the spatial discretization of the equation. The spatial discretization is, simply speaking, the second order ENO finite difference with subcell resolution near the interface. Our main interest is on the temporal discretization of the equation...

We derive a new model for seawater intrusion phenomena in free aquifers. It combines the efficiency of the sharp interface approach with the physical realism of the diffuse interface one. More precisely, a phase field is used as an intermediate variable for including the exchanges between the characteristic layers of the aquifer (salt water, fresh water, unsaturated zone). The threedimensional ...

We develop in this paper a new framework for discrete calculus of variations when the actions have densities involving an arbitrary discretization operator. We deduce the discrete Euler-Lagrange equations for piecewise continuous critical points of sampled actions. Then we characterize the discretization operators such that, for all quadratic lagrangian, the discrete Euler-Lagrange equations co...

In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional quasi-linear parabolic partial (PDEs), which is related to FBSDEs from Pardoux-Peng theory. The rely on a process by minimizing path-wise difference between two discrete processes, are defined time discretization DNN r...

A high-order Galerkin Least-Squares (GLS) finite element discretization is combined with massively parallel implicit solvers. The stabilization parameter of the GLS discretization is modified to improve the resolution characteristics and the condition number for the high-order interpolation. The Balancing Domain Decomposition by Constraints (BDDC) algorithm is applied to the linear systems aris...

This talk deals with a remarkable integrable discretization of the SO(3) Euler top introduced in [1] by R. Hirota and K. Kimura. A class of implicit discretizations of the Euler top sharing the integrals of motion with the continuous system has been presented and studied in [2]. The Hirota-Kimura discretization of the Euler top leads to an explicit map. Its integrability is proven by finding tw...

We develop time-splitting finite difference methods, using implicit Backward-Euler and semi-implicit Crank-Nicolson discretization schemes, to study the spin-orbit coupled spinor Bose Einstein condensates with coherent coupling in quasi-one quasi-two-dimensional traps. The split equations involving kinetic energy operators are solved either time-implicit or methods. explicitly method for pseudo...

In this article, we investigate and analyze new methods for the numerical solution of three-dimensional nonlocal evolution problem arising in viscoelastic mechanics. Then these combine Galerkin finite element (FEMs) spatial discretization with corresponding alternating direction implicit (ADI) algorithms, based on backward Euler (BE) method Crank-Nicolson (CN) method, respectively, from which, ...