Abstract In this contribution, it is demonstrated that the mesh sensitivity of linear elastic Reissner–Mindlin finite‐element plate formulations can be significantly reduced by using a Petrov–Galerkin‐based approach. contrast to usual Bubnov–Galerkin method, Petrov–Galerkin methods are generally characterized fact test function and trial approximated different shape functions. To provide an ove...

The objective of this paper is to provide the theoretical background and illustrative examples for elastic buckling analysis of cold-formed steel members with general boundary conditions as implemented in the forthcoming update to CUFSM. CUFSM is an open source finite strip elastic stability analysis program freely distributed by the senior author. Although the finite strip method presents a ge...

Let Ω be an open, simply connected, and bounded region in R, d ≥ 2, and assume its boundary ∂Ω is smooth. Consider solving an elliptic partial differential equation −∆u + γu = f over Ω with a Neumann boundary condition. The problem is converted to an equivalent elliptic problem over the unit ball B, and then a spectral Galerkin method is used to create a convergent sequence of multivariate poly...

In this report a general approach to algebraic multigrid methods for problems arising from the nite element discretization of a second order, self-adjoint, elliptic partial diierential equation is proposed. Special attention is paid to the coarsening process and the transfer operators. In order to construct a more exible method an auxiliary matrix is introduced which represents a virtual nite e...

This paper is concerned with a numerical solution for the scattering problem by an unbounded rough surface, which is referred to as a non-local perturbation of an infinite plane surface such that the whole surface lies within a finite distance of the original plane. A new and innovative spectral method is proposed to solve the unbounded rough surface scattering problem. The method uses a transf...

The Sinc-Galerkin method is presented as a new and potentially useful extension of the spectral method in numerical oceanography. To describe and illustrate the technique , a Sinc-Galerkin procedure is used to infer the sensitivity of wind-driven subsur-face currents in coastal regions and semi-enclosed seas when the vertical eddy viscosity coeecient is represented as a continuously diierentiab...

We extend the definition of the classical Jacobi polynomials withindexes α,β > −1 to allow α and/or β to be negative integers. We show that the generalized Jacobi polynomials, with indexes corresponding to the number of boundary conditions in a given partial differential equation, are the natural basis functions for the spectral approximation of this partial differential equation. Moreover, the...

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously nonhomogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for ...

We propose and analyze a finite element method for a semi– stationary Stokes system modeling compressible fluid flow subject to a Navier– slip boundary condition. The velocity (momentum) equation is approximated by a mixed finite element method using the lowest order Nédélec spaces of the first kind. The continuity equation is approximated by a standard piecewise constant upwind discontinuous G...

Abstract. The radiative transfer equation (RTE) occurs in a wide variety of applications. In this paper, we study discrete-ordinate discontinuous Galerkin methods for solving the RTE. The numerical methods are formed in two steps. In the first step, the discrete ordinate technique is applied to discretize the integral operator for the angular variable, resulting in a semi-discrete hyperbolic sy...