Related papers: An enhanced single Gaussian point continuum finite…
In this work, we provide the first strong convergence result of numerical approximation of a general second order semilinear stochastic fractional order evolution equation involving a Caputo derivative in time of order $\alpha\in(\frac 34,…
Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational…
In this article we present a refined convergence analysis for a second order accurate in time, fourth order finite difference numerical scheme for the 3-D Cahn-Hilliard equation, with an improved convergence constant. A modified backward…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
We present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained…
For the Stokes equation over 2D and 3D domains, explicit a posteriori and a priori error estimation are novelly developed for the finite element solution. The difficulty in handling the divergence-free condition of the Stokes equation is…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
In this paper, we introduce a new finite element method for solving the Stokes equations in the primary velocity-pressure formulation. This method employs $H(div)$ finite elements to approximate velocity, which leads to two unique…
We study a finite element approximation of a coupled fluid-structure interaction consisting of a three-dimensional incompressible viscous fluid governed by the unsteady Stokes equations and a two-dimensional elastic plate. To avoid the use…
Numerically robust algorithmic formulations suitable for rate-independent crystal plasticity are presented. They cover classic local models as well as gradient-enhanced theories in which the gradients of the plastic slips are incorporated…
The advancements in additive manufacturing (AM) technology have allowed for the production of geometrically complex parts with customizable designs. This versatility benefits large-scale space-frame structures, as the individual design of…
We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the…
We present an approach for synthesising observational data with elastodynamic finite element models by extending the statistical finite element method (statFEM) framework. The proposed formulation adopts a Bayesian filtering approach to…
This paper proposes a systematic and novel component level co-rotational (CR) framework, for upgrading existing 3D continuum finite elements to flexible multibody analysis. Without using any model reduction techniques, the high efficiency…
We present a novel cell-centered direct Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on unstructured triangular meshes that is high order accurate in space and time and that also allows for time-accurate local time stepping…
We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…
We present a new type of triangular $C^1$ finite elements developed for the plane strain crack problems within the simplified strain gradient elasticity (SGE). The finite element space contains a conventional fifth-degree polynomial…
Automatic differentiation (AD) is an ensemble of techniques that allow to evaluate accurate numerical derivatives of a mathematical function expressed in a computer programming language. In this paper we use AD for stating and solving solid…
Nowadays integration of mass matrix components in the element domain is performed using various numerical integration schemes, each one possess different level of accuracy, alters in number of integration (Gauss) points and requires…