The finite-strip method (FSM) is a hybrid technique which combines spectral and finite-element methods. Finite-element approximations are made for each mode of a finite Fourier series expansion. The Galerkin formulated method is set apart from other weighted-residual techniques by the selection of two types of basis functions, a piecewise linear interpolating function and a trigonometric functi...

We study practical strategies for estimating numerical errors in scalar outputs calculated from unsteady simulations of convection-dominated flows, including those governed by the compressible Navier–Stokes equations. The discretization is a discontinuous Galerkin finite element method in space and time on static spatial meshes. Time-integral quantities are considered for scalar outputs and the...

This paper presents a new particle method in LS-DYNA for the severe deformation and failure analyses of solid mechanics problems. The new formulation is first established following a standard meshfree Galerkin approach for a solving of the partial differential equation of linear elastic problems. A smoothed displacement field is introduced to the Galerkin formulation and leads to a regularized ...

this article studied static deflection, natural frequency and nonlinear vibration of a clamped-clamped microbeam under discontinues electrostatic actuation. the electrostatic actuation was induced by applying ac-dc voltage between the microbeam and electrode plate. in contrast to previous works, it was assumed that length of the electrode plate was smaller than that of the microbeam. in additio...

In numerical simulations, accounting for uncertainties in input quantities and keeping track of the resulting outcomes has become an important issue in recent years. In this talk we introduce an engineering application of uncertainty quantification for the aeroacoustic mechanisms in cavity flows under uncertain inputs. We introduce the stochastic Galerkin (SG) method and apply it to the compres...

In this paper we apply the generalized Taylor–Galerkin finite element model to simulate bore wave propagation in a domain of two dimensions. For stability and accuracy reasons, we generalize the model through the introduction of four free parameters. One set of parameters is rigorously determined to obtain the high-order finite element solution. The other set of free parameters is determined fr...

In this article we consider the development of discontinuous Galerkin finite element methods for the numerical approximation of the compressible Navier–Stokes equations. For the discretization of the leading order terms, we propose employing the generalization of the symmetric version of the interior penalty method, originally developed for the numerical approximation of linear self-adjoint sec...

Motivated by the Discontinous Petrov-Galerkin method from [Numer. Methods Partial Differential Equations, 27 (2011), 70–105] by Demkowicz and Gopalakrishnan, we study a variational formulation of second order elliptic equations in mixed form, that is obtained by piecewise integrating one of the two equations in the system w.r.t. a partition of the domain into mesh cells. We apply a Petrov-Galer...

A Finite Point Method (FPM) based on a weighted least squares interpolation is presented for the simulation of electroosmotic transport in capillaries. This method requires no mesh and involves no Galerkin-type integration, making it more computationally efficient than the traditional finite element method. The FPM has been employed to solve the non-linear Poisson-Boltzmann equation for charge ...

Numerical manifold method was applied to directly solve Navier-Stokes N-S equations for incompressible viscous flow in this paper, and numerical manifold schemes for N-S equations coupled velocity and pressure were derived based on Galerkin weighted residuals method as well. Mixed cover with linear polynomial function for velocity and constant function for pressure was employed in finite elemen...