automatic mesh generation and adaptation by using contours a general and efficient remeshing algorithm is presented for the discretization of arbitrary planar domains into triangular elements in consistency with the given node spacing funstion the contour lines of the node spacing function at suitable calculated levels provide the natural lines of division of the problem domain into subregions where finite elements meshes of different element sizes zre generated using the available general purpose mesh generators

the h text p version of the finite element method for domains with curved boundaries this paper analyzes the convergence of the h text p version of the finite element method for elliptic problems on curved domains it proves that when the boundary of the domain is piecewise analytic boundary conditions are piecewise analytic and the sides of the elements are analytic the h text p version has an exponential rate of convergence numerical computations are included the paper generalizes the results previously obtained by the authors the h text p version of finite element method part 1 the basic approximation results comp mech 1 1986 pp 21 41 the h text p version of finite element method part 2 general results and applications comp mech 1 1986 pp 203 220

adaptive remeshing and h p domain decomposition abstract the h p version of the finite element method combines local mesh refinement with an increase of the shape functions polynomial degree this paper presents a method which uses an h p approximation for a domain decomposition with fully overlapping domains allowing c 0 continuous approximation for geometrically incompatible mesh refinement to be obtained the method is applied to a reaction diffusion problem resulting from semiconductor process simulation in numerical examples it is demonstrated that this approach is well suited for problems with sharp interior layers or shock like behaviour

an a posteriori error estimator for the p and hp versions of the finite element method an a posteriori error estimator is proposed in this paper for the p and hp versions of the finite element method in two dimensional linear elastostatic problems the local error estimator consists in an enhancement of an error indicator proposed by bertoti and szabo int j numer meth engng 1998 42 561 587 which is based on the minimum complementary energy principle in order to obtain the local error estimate this error indicator is corrected by a factor which depends only on the polynomial degree of the element the proposed error estimator shows a good effectivity index in meshes with uniform and non uniform polynomial distributions especially when the global error is estimated furthermore the local error estimator is reliable enough to guide p and hp adaptive refinement strategies

error estimates for the combinedh andp versions of the finite element method in theh version of the finite element method convergence is achieved by refining the mesh while keeping the degree of the elements fixed on the other hand thep version keeps the mesh fixed and increases the degree of the elements in this paper we prove estimates showing the simultaneous dependence of the order of approximation on both the element degrees and the mesh in addition it is shown that a proper design of the mesh and distribution of element degrees lead to a better than polynomial rate of convergence with respect to the number of degrees of freedom even in the presence of corner singularities numerical results comparing theh version p version and combinedh p version for a one dimensional problem are presented

construction of shape functions for the h and p versions of the fem using tensorial product this paper presents an uniform and unified approach to construct h and p shape functions for quadrilaterals triangles hexahedral and tetrahedral based on the tensorial product of one dimensional lagrange and jacobi polynomials the approach uses indices to denote the one dimensional polynomials in each tensorization direction the appropriate manipulation of the indices allows to obtain hierarchical or non hierarchical and inter element c continuous or non continuous bases for the one dimensional elements quadrilaterals triangles and hexahedral the optimal weights of the jacobi polynomials are determined the sparsity profiles of the local mass and stiffness matrices plotted and the condition numbers calculated a brief discussion of the use of sum factorization and computational implementation is considered

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

a parallel adaptive strategy for hp finite element computations abstract in this work a new three step adaptive strategy for hp finite element discretizations is presented techniques for parallelizing these calculations on distributed memory multiprocessor computers are also developed numerical examples are used to demonstrate convergence properties and parallel efficiencies orders of magnitude reduction in computational efficiency over conventional methods are observed

analysis of the zienkiewicz zhu a posteriori error estimator in the finite element method an a posteriori error estimator for finite element analysis proposed by zienkiewicz and zhu is analysed and shown to be effective and convergent in addition we analyse wider classes of estimators of which the zienkiewicz zhu estimator is a special case it is shown that some of these estimators will be asymptotically exact numerical evidence is presented supporting the analysis

applications of lobatto polynomials to an adaptive finite element method a posteriori error estimates for hp adaptivity and grid to grid interpolation hp adaptive finite element codes require methods for estimating the error at several spatial orders and for interpolating solutions between grids lobatto polynomial based techniques are presented for both an interpolation error based error estimation strategy for a posteriori error estimates is generalized to yield asymptotically exact error estimates one order higher than the computed solution the estimates involve high order derivatives of the solution that must be approximated from the computed solution differentiating a taylor like series for error in the lobatto interpolant and using the weak form of the equations yields the correct derivative approximations this leads to a more robust order selection strategy interpolation between grids is done over each element using the lobatto interpolating polynomial explicit formulas for the inverse of the resulting lobatto interpolation matrices are given computational results illustrate the theory

an adaptive hp version of the finite element method applied to flame propagation problems this paper describes an adaptive hp version mesh refinement strategy and its application to the finite element solution of one dimensional flame propagation problems the aim is to control the spatial and time discretization errors below a prescribed error tolerance at all time levels in the algorithm the optimal time step is first determined in an adaptive manner by considering the variation of the computable error in the reaction zone later the method uses a p version refinement till the computable a posteriori error is brought down below the tolerance during the p version if the maximum allowable degree of approximation is reached in some elements of the mesh without satisfying the global error tolerance criterion then conversion from p to h version is performed in the conversion procedure a gradient based non uniform h version refinement has been introduced in the elements of higher degree approximation in this way p version and h version approaches are used alternately till the a posteriori error criteria are satisfied the mesh refinement is based on the element error indicators according to a statistical error equi distribution procedure numerical simulations have been carried out for a linear parabolic problem and premixed flame propagation in one space dimension 1997 john wiley sons ltd

analytic propagation model for wireless body area networks wave propagation in wireless body area networks wban is analytically modeled as a polarized point source close to an elliptic lossy dielectric cylinder using the fourier transform along the axes the expansion in terms of mathieu functions in cross section and the impedance boundary condition ibc on surface the field distribution outside the cylinder can be formulated in particular the path gain of propagation around the human body is described in detail for 915 mhz and 2 40 ghz bands toward industrial scientific and medical ism applications

adaptive hpq finite element methods of hierarchical models for plate and shell like structures abstract a four step adaptive strategy for hpq finite element approximations of hierarchical models of the thin plate and shell like structures is derived based on a priori and a posteriori error estimations this strategy controls three parameters the model level q the mesh size h and the approximation order p so as to produce quasi optimal hierarchical models and finite element meshes numerical results are given supporting the theoretical results

an adaptive h refinement using transition element for plate bending problems an adaptive h refinement procedure utilizing compatible 5 to 7 node quadrilateral transition elements together with 4 node elements is presented for reissner mindlin plate bending problems by introducing the transition elements which have physical midside nodes some difficulties associated with imposing displacement constraints on irregular nodes to enforce interelement compatibility in common adaptive h refinement on quadrilateral mesh are easily overcome numerical examples are presented to show the effectiveness of using the transition elements for the adaptive h refinement

a new triangular and tetrahedral basis for high order hp finite element methods in this paper we describe the foundations of a new hierarchical modal basis suitable for high order hp finite element discretizations on unstructured meshes it is based on a generalized tensor product of mixed weight jacobi polynomials the generalized tensor product property leads to a low operation count with the use of sum factorization techniques variable p order expansions in each element are readily implemented which is a crucial property for efficient adaptive discretizations numerical examples demonstrate the exponential convergence for smooth solutions and the ability of this formulation to handle easily very complex two and three dmensional computational domains employing standard meshes

r adaptive mesh generation for shell finite element analysis an r adaptive method or moving grid technique relocates a grid so that it becomes concentrated in the desired region this concentration improves the accuracy and efficiency of finite element solutions we apply the r adaptive method to computational mesh of shell surfaces which is initially regular and uniform the r adaptive method given by liao and anderson appl anal 44 1992 285 aggregate the grid in the region with a relatively high weight function without any grid tangling the stress error estimator is calculated in the initial uniform mesh for a weight function however since the r adaptive method is a method that moves the grid shell surface geometry error such as curvature error and mesh distortion error will increase therefore to represent the exact geometry of a shell surface and to prevent surface geometric errors we use the naghdi s shell theory and express the shell surface by a b spline patch in addition using a nine node element which is relatively less sensitive to mesh distortion we try to diminish mesh distortion error in the application of an r adaptive method in the numerical examples it is shown that the values of the error estimator for a cylinder hemisphere and torus in the overall domain can be reduced effectively by using the mesh generated by the r adaptive method also the reductions of the estimated relative errors are demonstrated in the numerical examples in particular a new functional is proposed to construct an adjusted mesh configuration by considering a mesh distortion measure as well as the stress error function the proposed weight function provides a reliable mesh adaptation method after a parameter value in the weight function is properly chosen

a dual primal feti method for incompressible stokes equations in this paper a dual primal feti method is developed for incompressible stokes equations approximated by mixed finite elements with discontinuous pressures the domain of the problem is decomposed into nonoverlapping subdomains and the continuity of the velocity across the subdomain interface is enforced by introducing lagrange multipliers by a schur complement procedure the solution of an indefinite stokes problem is reduced to solving a symmetric positive definite problem for the dual variables i e the lagrange multipliers this dual problem is solved by the conjugate gradient method with a dirichlet preconditioner in each iteration step both subdomain problems and a coarse level problem are solved by a direct method it is proved that the condition number of this preconditioned dual problem is independent of the number of subdomains and bounded from above by the square of the product of the inverse of the inf sup constant of the discrete problem and the logarithm of the number of unknowns in the individual subdomains numerical experiments demonstrate the scalability of this new method

adaptive wavelet enriched hierarchical finite element model for polycrystalline microstructures abstract this paper proposes an adaptive wavelet enriched hierarchical finite element model fem to enhance computational efficiency and solution accuracy for heterogeneous domains of anisotropic elastic materials it is motivated by the need to overcome shortcomings of conventional methods like the standard fem or fast fourier transformation fft based method for analyzing deformation in large polycrystalline microstructures the multi resolution wavelet functions are advantageous for selection of an optimal set of functions that can adaptively enrich the solution space with a prescribed level of accuracy the proposed method introduces a discretization space that conforms to the profile of the solution sought the method engages a second generation family of wavelets with a lifting scheme to generate hierarchical interpolation functions an iterative algorithm efficiently calculates estimates of the solution from the previous iterate using a modified jacobi method the adaptive fe method performs significantly better than uniformly refined fem in validation tests with focus on the convergence rate and error mitigation a polycrystalline microstructure with elastically anisotropic grains is simulated by the adaptive wavelet enriched hierarchical method showing high convergence rates

an explicit a posteriori error indicator for electromagnetic finite element boundary integral analysis within the finite element method fem there is always an error associated with the solution quantifying this error is a very important aspect of fe analysis since it can increase confidence in a solution and can be used to drive adaptive refinements of the discretization optimizing the quality of the solution relative to the number of degrees of freedom and in turn reducing computational cost this paper presents an a posteriori error indicator for time harmonic electromagnetic analysis in three dimensions when using a galerkin fe approach with curl conforming elements and including a nonlocal boundary integral boundary condition as well as a dominant mode port boundary condition the error indicator is residual based of an explicit nature and constitutes a bound on an error energy measure the error indicator is evaluated by presenting results relating to common microwave engineering applications which shows that it can be used successfully to estimate the relative error distribution and that it can successfully serve within an adaptive algorithm

automated adaptive two dimensional system for the hp version of the finite element method this paper presents an automated adaptive finite element modelling system based on the hp version of the finite element method error estimation and correction indication procedures with an automatic mesh generator and a p version analysis code are combined to provide a computationally efficient modelling environment error prediction techniques are employed to find the best combination of finite element discretization h and overall polynomial order p needed to achieve the prescribed level of accuracy the automated adaptive modelling results demonstrate the capability of the modelling system of predicting discretizations to perform a p version finite element analysis to achieve prescribed levels of accuracy in the most efficient manner

effects of element distortions on the performance of isoparametric elements we discuss the effects of element distortions on the performance of displacement based isoparametric quadrilateral finite elements suitable example problems for both the lagrangian and the serendipity types of elements are used to show numerically the effects of element distortions the effects of angular and curved edge distortions are evaluated analytically in terms of the abilities of the elements to represent exactly various polynomial displacement fields we then solve a plane stress problem adaptively to demonstrate the effect of element distortions on the accuracy of the stress distribution the conclusion is that the lagrangian elements are not affected by angular distortions and are therefore the more reliable elements for general use

error estimators using global local methods error estimators were derived using global local and refined global local finite element methods and an extrapolation technique the proposed error estimators are to be used in estimating the global error energy norm local error energy norm and nodal displacement error these error estimators were applied to three numerical examples the results clearly demonstrated that these error estimators are of high quality

geometrical interpretation for error estimation in finite element analysis abstract geometrical interpretation for the error estimation procedure in finite element analysis is discussed the proposed description is based on the superconvergent properties of certain points in the finite element model and discrete geometrical objects which are characteristic for a discrete representation the new local error estimator is valid for triangular and quadrilateral elements and is strictly bounded in both nonsingular and singular cases preliminary calculations indicate that the new error estimator can be applied for adaptive refinement analysis especially in geometrically nonlinear shell problems where the control of both physical and geometrical fields in adaptive calculations is very important

adaptive s method for linear elastostatics abstract a methodology has been developed to simultaneously treat phenomena at several scales the key features of the method are i a detailed error diagnosis which identifies critical regions and ii a feedback procedure which overlays portions of the finite element mesh where unacceptable errors have been identified by local finite element mesh es and then subsequently improves the quality of the solution in the global and local response until the desired level of accuracy is achieved the method can be routinely used as a global local method and or as an adaptive technique which provides a measure of reliability of global and local computations numerical experiments for problems in homogeneous and heterogeneous laminated composites media are presented to validate the present formulation

an automatic procedure with a control of accuracy for finite element analysis in 2d elasticity abstract this paper gives a procedure for an automation of the entire finite element analysis for 2d or axisymmetric elastic structures with a control of accuracy the user describes the problem and the level of desired accuracy the procedure then provides an approximate solution for a minimal computation cost this procedure uses an error measure based on the constitutive relation 1 5 and an efficient adaptive technique 6 which automatically take account of the regions of stress concentration examples are presented for discretizations using 3 or 6 node triangular elements

effective and practical h p version adaptive analysis procedures for the finite element method two practical and effective h p type finite element adaptive procedures are presented the procedures allow not only the final global energy norm error to be well estimated using hierarchic p refinement but in addition give a nearly optimal mesh the design of this is guided by the local information computed on the previous mesh the desired accuracy can always be obtained within one or at most two h p refinements the rate of convergence of the adaptive h p version analysis procedures has been tested for some examples and found to be very strong the presented procedures can easily be incorporated into existing p or h type code structures

the superconvergent patch recovery and a posteriori error estimates part 2 error estimates and adaptivity in this second part of the paper the issue of a posteriori error estimation is discussed in particular we derive a theorem showing the dependence of the effectivity index for the zienkiewicz zhu error estimator on the convergence rate of the recovered solution this shows that with superconvergent recovery the effectivity index tends asymptotically to unity the superconvergent recovery technique developed in the first part of the paper1 is the used in the computation of the zienkiewicz zhu error estimator to demonstrate accurate estimation of the exact error attainable numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient stress error estimation several examples of the performance of the error estimator in adaptive mesh refinement are also presented

pollution error in the h version of the finite element method and the local quality of the recovered derivatives abstract in this paper we address the quality of the solution derivatives which are recovered from finite element solutions by local averaging schemes as an example we consider the zienkiewicz zhu superconvergent patch recovery scheme the zz spr scheme and we study its accuracy in the interior of the mesh for finite element approximations of solutions of laplace s equation in polygonal domains we will demonstrate the following 1 in general the accuracy of the derivatives recovered by the zz spr or any other local averaging scheme may not be higher than the accuracy of the derivatives computed directly from the finite element solution 2 if the mesh is globally adaptive i e it is nearly equilibrated in the energy norm then we can practically always gain in accuracy by employing the recovered derivatives instead of the derivatives computed directly from the finite element solution 3 it is possible to guarantee that the recovered solution derivatives have higher accuracy than the derivatives computed directly from the finite element solution in any patch of elements of interest by employing a mesh which is adaptive only with respect to the patch of interest i e it is nearly equilibrated in a weighted energy norm 4 in practice we are often interested in obtaining highly accurate derivatives or heat fluxes stresses etc only in a few critical regions which are identified by a preliminary analysis a grid which is adaptive only with respect to the critical regions of interest may be much more economical for this purpose because it may achieve the desired accuracy by employing substantially fewer degrees of freedom than a globally adaptive grid which achieves comparable accuracy in the critical regions

adaptive finite element boundary integral analysis for electromagnetic fields in 3 d this paper presents a complete adaptive finite element boundary integral fe bi analysis scheme for the time harmonic electromagnetic analysis of three dimensional inhomogeneous scatterers radiators in free space the adaptive scheme is based on an fe bi formulation which yields electric and magnetic field solutions simultaneously it employs a posteriori error estimates which exploit the availability of both field solutions and estimates error distributions and global solution quality for the electric and magnetic fields separately it automatically determines which elements should be refined in order to equi distribute the estimated error based on the type of refinement requested h p or hp this automatic determination is based on extrapolating the elemental error estimates the algorithm terminates when specified tolerance levels are reached by the electric and or magnetic field global solution quality estimates the only required user specifications within the algorithm are the termination tolerances and the types of refinements to effect results are presented which show that within the scope of the presented error measures significant reductions in computational cost may be achieved the proposed scheme could be used with other types of error estimates and it could be adapted to other fe or fe bi formulations