In this paper we present the efficient parallel implementation of elastoplastic problems based on the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. This approach allow us to use parallel solution and compute this nonlinear problem on the supercomputers and decrease the solution time and compute problems with millions of DOFs. In our approach we consider a...

A quadratic optimal control problem governed by parabolic equations with integral constraints is considered. A fully discrete finite element scheme is constructed for the optimal control problem, with finite elements for the spatial but the backward Euler method for the time discretisation. Some superconvergence results of the control, the state and the adjoint state are proved. Some numerical ...

A second-order singularly perturbed parabolic equation in one space dimension is considered. For this equation, we give computable a posteriori error estimates in the maximum norm for two semidiscretisations in time and a full discretisation using P1 FEM in space. Both the Backward-Euler method and the Crank-Nicolson method are considered, and certain critical details of the implementation are ...

In standard deformable object simulation in computer animation, all the mesh elements or vertices are timestepped synchronously, i.e., under the same timestep. Previous asynchronous methods have been largely limited to explicit integration. We demonstrate how to perform spatially-varying timesteps for the widely popular implicit backward Euler integrator. Spatiallyvarying timesteps are useful w...

We consider the problem of parameter estimation for a class continuous-time state space models (SSMs). In particular, we explore case partially observed diffusion, with data also arriving according to diffusion process. Based upon standard identity score function, two particle filter based methodologies estimate function. Both methods rely on an online algorithm as described, e.g., in [P. Del M...

It is shown that for a parabolic problem with maximal Lp-regularity (for 1 < p < ∞), the time discretization by a linear multistep method or Runge–Kutta method has maximal `p-regularity uniformly in the stepsize if the method is A-stable (and satisfies minor additional conditions). In particular, the implicit Euler method, the Crank–Nicolson method, the second-order backward difference formula ...

The time-dependent Stokes equations in twoor three-dimensional bounded domains are discretized by the backward Euler scheme in time and finite elements in space. The error of this discretization is bounded globally from above and locally from below by the sum of two types of computable error indicators, the first one being linked to the time discretization and the second one to the space discre...

n this paper, we have implemented the finite element method for numerical solution of a boundary and initial value problems, mainly on solving one two-dimensional advection-diffusion equation with constant parameters. In doing so, basic idea is to first rewrite problem as variational equation, then seek approximation from space continuous piece-wise linear’s. This discretization procedure resul...

Abstract In this paper, we focus on the penalty finite element method for non stationary porous media model. We begin by showing existence and uniqueness of solution initial problem. Error estimates velocity pressure are obtained via energy method. introduce a time discretization use backward Euler scheme combined with fully discrete to approximate penalized problem establish an error estimate ...

Efficient and accurate numerical methods are presented for computing ground states and dynamics of the three-dimensional (3D) nonlinear relativistic Hartree equation both without and with an external potential. This equation was derived recently for describing the mean field dynamics of boson stars. In its numerics, due to the appearance of pseudodifferential operator which is defined in phase ...