The a-posteriori error evaluation based on differential approximation of a finite-difference scheme and adjoint equations is addressed. The differential approximation is composed of primal equations and a local truncation error determined by a Taylor series in Largange form. This approach provides the feasibility of both refining the solution and using the Holder inequality for asymptotic bound...

Maxwell’s equations in a bounded Debye medium are formulated in terms of the standard partial differential equations of electromagnetism with a Volterra-type history dependence of the polarization on the electric field intensity. This leads to Maxwell’s equations with memory. We make a correspondence between this type of constitutive law and the hereditary integral constitutive laws from linear...

This paper presents a convergence analysis of the multi point flux approximation control volume method, MPFA, in two space dimensions. The MPFA version discussed here is the so–called O–method on general quadrilateral grids. The discretization is based on local mappings onto a reference square. The key ingredient in the analysis is an equivalence between the MPFA method and a mixed finite eleme...

The simulation of impact damage in laminated composite plates presents many challengesto modelers. Local failure takes the form of various fracture processes. For compositesthis is further complicated because the various modes can strongly interact with each other.Another modeling challenge particular to composite materials is that it is often necessaryto simulate the struct...

The work presented in this paper is part of the cooperative research project AUTO–OPT carried out by twelve partners from the automotive industries. One major work package concerns the application of data mining methods in the area of automotive design. Suitable methods for data preparation and data analysis are developed. The objective of the work is the re–use of data stored in the crash–simu...

This paper presents a new isogeometric mortar contact formulation based on an extended finite element interpolation to capture physical pressure discontinuities at the contact boundary. The so called two-half-pass algorithm is employed, which leads to an unbiased formulation and, when applied to the mortar setting, has the additional advantage that the mortar coupling term is no longer present ...

This paper considers a finite-element approximation of a second-order selfadjoint elliptic equation in a region flcR" (with n = 2 or 3) having a curved boundary dQ on which a Neumann or Robin condition is prescribed. If the finite-element space denned over D, a union of elements, has approximation power h in the L norm, and if the region of integration is approximated by Q* with dist (Q, £?*) =...

In a paper by R. Durán, A. Lombardi, and the authors (2007) the finite element method was applied to a non-homogeneous Neumann problem on a cuspidal domain Ω ⊂ R2, and quasi-optimal order error estimates in the energy norm were obtained for certain graded meshes. In this paper, we study the error in the L2 norm obtaining similar results by using graded meshes of the type considered in that pape...

The paper is devoted to the eigenvalue problem for a second order strongly elliptic operator. The problem is considered on curved domains, which require interpolated boundary conditions in approximating finite element formulation. The necessary triangulations for solving the eigenvalue problem consists of isoparametric elements of degree n, where n is any integer greater than two. An approximat...

.............................................................................................................................. ii Dedication .......................................................................................................................... iv Acknowledgments............................................................................................................... v V...