A time-domain, finite element–boundary integral (FE–BI) method is presented for analyzing electromagnetic (EM) scattering from two-dimensional (2-D) inhomogeneous objects. The scheme’s finite-element component expands transverse fields in terms of a pair of orthogonal vector basis functions and is coupled to its boundary integral component in such a way that the resultant finite element mass ma...

In this paper, we consider the error estimates of the numerical solutions of a class of fourth order linear-quadratic elliptic optimal control problems by using mixed finite element methods. The state and co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order k (k ≥ 1). L and L-error estimate...

A recently developed wave based method (WBM) has proven to be a computationally efficient tool for analysing steady-state lowand mid-frequency acoustic problems. The method is based on an indirect Trefftz approach, in that the dynamic pressure field is approximated by wave functions, which are exact solutions of the governing Helmholtz equation. Several case studies have shown that the WBM exhi...

Mathematical modelling of welding phenomena is very complex: involving melt pool phenomena, solidification, weldability analysis, microstructure evolution in the heat affected zone, welding heat-flow simulation, electrical-thermal-mechanical simulation etc. Some interactions between these processes are included in Fig. 1. Each topic alone can be intellectually challenging and too hard to be inv...

Most grinding problems cannot be solved analytically, therefore extensive numerical solutions are required by using appropriate numerical techniques such as the finite element method (FEM). In this study, the well-known finite element software, ADINA, was used to predict the phase transformation of a workpiece subjected to surface grinding. The process was considered to be two-dimensional and t...

In this paper, we review the existing interpolation functions and introduce a finite element interpolation function to be used in the immersed boundary and finite element methods. This straightforward finite element interpolation function for unstructured grids enables us to obtain a sharper interface that yields more accurate interfacial solutions. The solution accuracy is compared with the ex...

A three-dimensional finite element implementation of a simple nonassociative Drucker-Prager plasticity model with strong discontinuity mode of localized deformation is formulated for small deformations. A strong discontinuity mode of localized deformation represents slip along a surface of zero measure, whereas a weak discontinuity mode of localized deformation represents shear within a band of...

It is often found that tangent-stiffness finite element solutions for elastic-plastic materials exhibit much too stiff a response in the fully plastic range. This is most striking for the perfectly plastic material idealization, in which case a limit load exists within conventional small displacement gradient assumptions. However, finite element solutions often exceed the limit load by substant...

This paper presents an overview of both T-Trefftz and F-Trefftz finite element methods (FEM) and its application in various engineering problems. Recent developments on the T-Trefftz finite element formulation of nonlinear problems of minimal surface, F-Trefftz methods for composite, skin tissue, and functionally graded materials are described. Formulations for all cases are derived by means of...

This paper is devoted to the study of finite element approximations of variational inequalities with a special nonlinearity coming from boundary conditions. After re-writing the problems in the form of variational inequalities, a fixed point strategy is used to show existence of solutions. Next we prove that the finite element approximations for the Stokes and Navier Stokes equations converge r...