Granular flows are systems of complex dry particulates whose behavior is difficult to predict during sliding contact. Existing computational tools used to simulate granular flows are particle dynamics, cellular automata (CA), and continuum modeling. In the present investigation, another numerical tool—the explicit finite element method (FEM)—is analyzed as a potential technique for simulating g...

Abstract This paper studies fully discrete finite element approximations to the Navier–Stokes equations using inf-sup stable elements and grad-div stabilization. For time integration, two implicit–explicit second-order backward differentiation formulae (BDF2) schemes are applied. In both, Laplacian is implicit while nonlinear term explicit, in first one, semiimplicit, second one. The stabilizat...

The goal of this paper is to define a procedure for bounding the error in a conforming finite element method. The new point is that this upper bound is fully explicit and can be computed locally. Numerical tests prove the efficiency of the method. It is presented here for the case of the Poisson equation and a first order finite element approximation.

In this paper, we consider a novel 3D visualization technique based on surface flattening for virtual colonoscopy. Such visualization methods could be important in virtual colonoscopy since they have the potential for non-invasively determining the presence of polyps and other pathologies. Further, we demonstrate a method which presents a surface scan of the entire colon as a cine, and affords ...

In this paper, an alternative approach for constructing an a posteriori error estimator for non-conforming approximation of scalar elliptic equation is introduced. The approach is based on the usage of post-processing conforming finite element approximation of the non-conforming solution . Then, the compatible a posteriori error estimator is defined by the local norms of difference between the ...

and Applied Analysis 3 Table 1: Solitary wave Amp. 0.3 and the errors in L2 and L∞ norms for u, Q 1 , Q 2 , and Q 3 at t = 20, h = 0.125, Δt = 0.1, and −40 ≤ x ≤ 60. Method Time Q 1 Q 2 Q 3 L 2 for u L∞ for u Our method 0 3.9797 0.8104 2.5787 0 0 4 3.9797 0.8104 2.5786 3.6304e − 004 5.2892e − 005 8 3.9797 0.8104 2.5786 7.2873e − 004 5.8664e − 005 12 3.9797 0.8104 2.5787 1.0817e − 003 6.3283e − ...

In this article, element free Galerkin method is used for static analysis of thin micro/nanoscale plates based on the nonlocal plate theory. The problem is solved for the plates with arbitrary boundary conditions. Since shape functions of the element free Galerkin method do not satisfy the Kronecker’s delta property, the penalty method is used to impose the essential boundary conditions. Discre...

Biofidelic numerical models require accurate geometry, material properties, representative loading conditions, and proper verification and validation based on relevant experimental studies. Imaging techniques such as CT or MRI are typically used to generate anatomically correct model geometry. Accurate biological material properties and constitutive models present a challenge s...

In the present study, a spectral finite element method is developed for free and forced transverse vibration of Levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. Levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. In the first step, the governing out-of-plane differential equations are tr...

We present a systematic canonical quantization procedure for lumped-element superconducting networks by using redundant configuration-space description. The algorithm is based on an original, explicit, and constructive implementation of the symplectic diagonalization positive semidefinite Hamiltonian matrices, particular instance Williamson's theorem. With it, we derive canonically quantized di...