This is a continued study on the solution of convection-diffusion equations with boundary layers. In our previous work, Part I, the solutions of the homogenenous singularly perturbed differential equations with Dirichlet boundary conditions are expressed in a series of particular solutions have been proposed, based on the separation of variables. In this study we extend our previous results to ...

This paper contains two main parts. First, applications of Trefftz finite element methods to mode III fracture problems are presented in this paper. Trial functions for electoelastic fields are presented for both regular element and cracked element. These functions are used in deriving Trefftz finite element formulation together with modified variational principle. The performance of the propos...

Generally, two approaches have been used to study the nonlinear wave-structure interaction in the context of offshore engineering in recent years. One is based on the Stokes perturbation procedure in the frequency domain and has been applied to weak-nonlinear problems. The other is based on a full nonlinear solution to the resulting wave field by a time-stepping procedure with boundary conditio...

We use the singular function boundary integral method (SFBIM) to solve two model fracture problems on the plane. In the SFBIM, the solution is approximated by the leading terms of the local asymptotic solution expansion, which are also used to weight the governing biharmonic equation in the Galerkin sense. The discretized equations are reduced to boundary integrals by means of the divergence th...

Modeling of elastic thin-walled beams, plates and shells as 1D and 2D boundary value problems is valid in undisturbed subdomains. Disturbances near supports and free edges, in the vicinity of concentrated loads and at thickness jumps cannot be described by 1D and 2D BVP’s. In these disturbed subdomains dimensional (d)-adaptivity and possibly model (m)-adaptivity have to be performed and coupled...

We present and analyze a non-standard finite element method based on element-local boundary integral operators that permits polyhedral element shapes as well as meshes with hanging nodes. The method employs elementwise PDE-harmonic trial functions and can thus be interpreted as a local Trefftz method. The construction principle requires the explicit knowledge of the fundamental solution of the ...

We present and analyze a non-standard finite element method based on elementlocal boundary integral operators that permits polyhedral element shapes as well as meshes with hanging nodes. The method employs elementwise PDE-harmonic trial functions and can thus be interpreted as a local Trefftz method. The construction principle requires the explicit knowledge of the fundamental solution of the p...