In this work, we consider the numerical solution of a distributed order subdiffusion model, arising in the modeling of ultra-slow diffusion processes. We develop a space semidiscrete scheme based on the Galerkin finite element method, and establish error estimates optimal with respect to data regularity in L2(Ω) and H1(Ω) norms for both smooth and nonsmooth initial data. Further, we propose two...

We propose an algorithm for the efficient parallel implementation of elastoplastic problems with hardening based on the so-called TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. We consider an associated elastoplastic model with the von Mises plastic criterion and the linear isotropic hardening law. Such a model is discretized by the implicit Euler method i...

The physically-based simulation of mechanical effects has been an important research topic in computer graphics for more than two decades. Classical methods in this field discretize Newton’s second law and determine different forces to simulate various effects like stretching, shearing, and bending of deformable bodies or pressure and viscosity of fluids, to mention just a few. Given these forc...

We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann–Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank...

We show that the Euler-discretization of nonlinear continuous-time model a single mast stacker crane is flat. The construction flat output based on transformation subsystem into linear time-variant discrete-time controller canonical form. Based derived output, which also function backward-shifts system variables, we discuss planning trajectories to achieve transition between two rest positions ...

In this paper, we consider the classical wave equation with time-dependent, spatially multiscale coefficients. We propose a fully discrete computational method in spirit of localized orthogonal decomposition space backward Euler scheme time. show optimal convergence rates and time beyond assumptions spatial periodicity or scale separation Further, an adaptive update strategy for time-dependent ...

It has been shown that the plastic response of many materials, including some metallic alloys, depends on the stress state. In this paper, we describe a plasticity model for isotropic materials, which is a function of the hydrostatic stress as well as the second and third invariants of the stress deviator, and present its finite element implementation, including integration of the constitutive ...

Abstract. In this paper, three-dimensional parabolic and pseudo-parabolic equations with classical, periodic and nonlocal boundary conditions are approximated by the full approximation backward Euler method, locally one dimensional and Douglas ADI splitting schemes. The stability with respect to initial conditions is investigated. We note that the stability of the proposed numerical algorithms ...

We consider an initialand Dirichlet boundaryvalue problem for a fourth-order linear stochastic parabolic equation, in two or three space dimensions, forced by an additive space-time white noise. Discretizing the space-time white noise a modeling error is introduced and a regularized fourthorder linear stochastic parabolic problem is obtained. Fully-discrete approximations to the solution of the...

In this paper, we study time discretizations of fully nonlinear parabolic differential equations. Our analysis uses the fact that the linearization along the exact solution is a uniformly sectorial operator. We derive smooth and nonsmooth-data error estimates for the backward Euler method, and we prove convergence for strongly A(θ)stable Runge–Kutta methods. For the latter, the order of converg...