adaptive finite element methods for parabolic problems vi analytic semigroups we continue our work on adaptive finite element methods with a study of time discretization of analytic semigroups we prove optimal a priori and a posteriori error estimates for the discontinuous galerkin method showing in particular that analytic semigroups allow long time integration without error accumulation

average rate of downlink heterogeneous cellular networks over generalized fading channels a stochastic geometry approach in this paper we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks the framework leverages recent application of stochastic geometry to other cell interference modeling and analysis the heterogeneous cellular network is modeled as the superposition of many tiers of base stations bss having different transmit power density path loss exponent fading parameters and distribution and unequal biasing for flexible tier association a long term averaged maximum biased received power tier association is considered the positions of the bss in each tier are modeled as points of an independent poisson point process ppp under these assumptions we introduce a new analytical methodology to evaluate the average rate which avoids the computation of the coverage probability pcov and needs only the moment generating function mgf of the aggregate interference at the probe mobile terminal the distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions including composite fading channels with small and mid scale fluctuations in addition our method can efficiently handle correlated log normal shadowing with little increase of the computational complexity the proposed mgf based approach needs the computation of either a single or a two fold numerical integral thus reducing the complexity of pcov based frameworks which require for general fading distributions the computation of a four fold integral

a modified stochastic perturbation method for stochastic hyperbolic heat conduction problems abstract the stochastic hyperbolic heat conduction problem is addressed the random field is approximated by using the karhunen loeve expansion truncated after a finite numbers of terms and a modified stochastic perturbation method mspm is proposed for the stochastic hyperbolic heat conduction problems the mspm is based on the stochastic perturbation theory and can provide the mean and covariance of the random temperature including some third and forth order terms compared with the original stochastic perturbation method the mspm is more accurate and is more convenient for the numerical implementation and hence is more applicable for the stochastic hyperbolic heat conduction problem two numerical examples demonstrate that the proposed method can provide very accurate results and can be used for the stochastic hyperbolic heat conduction problems

on discontinuous galerkin methods discontinuous galerkin methods have received considerable attention in recent years for problems in which advection and diffusion terms are present several alternatives for treating the diffusion and advective fluxes have been introduced this report summarizes some of the methods that have been proposed several numerical examples are included in the paper these present discontinuous galerkin solutions of one dimensional problems with a scalar variable results are presented for diffusion reaction problems and advection diffusion problems we discuss the performance of various formulations with respect to accuracy as well as stability of the method copyright 2003 john wiley sons ltd

moments based approach to the performance analysis of equal gain diversity in nakagami m fading in this letter an alternative moments based approach for the performance analysis of an l branch predetection equal gain combiner egc over independent or correlated nakagami m fading channels is presented exact closed form expressions are derived for the moments of the egc output signal to noise ratio snr while the corresponding moment generating function mgf is accurately approximated with the aid of pade spl acute approximants theory important performance criteria are studied the average output snr which is expressed in closed form both for independent and correlative fading and for arbitrary system parameters the average symbol error probability for several coherent noncoherent and multilevel modulation schemes and the outage probability which are both accurately approximated using the well known mgf approach the proposed mathematical analysis is illustrated by various numerical results and computer simulations have been performed to verify the validity and the accuracy of the theoretical approach

an asynchronous spacetime discontinuous galerkin finite element method for time domain electromagnetics abstract we present an asynchronous spacetime discontinuous galerkin asdg method for time domain electromagnetics in which space and time are directly discretized by using differential forms we express maxwell s equations and consequently their discontinuous galerkin discretization for arbitrary domains in spacetime the elements are discretized with electric and magnetic basis functions that are discontinuous across all inter element boundaries and can have arbitrary high and per element spacetime orders when restricted to unstructured grids that satisfy a specific causality constraint the method has a local and asynchronous solution procedure with linear solution complexity in terms of the number of elements we numerically investigate the convergence properties of the method for 1d to 3d uniform grids for energy dissipation an error relative to the exact solution and von neumann dissipation and dispersion errors two dimensional simulations demonstrate the effectiveness of the method in resolving sharp wave fronts

existence of at least three solutions of a second order three point boundary value problem abstract we study existence of at least three solutions in the presence of two lower and two upper solutions of some second order nonlinear three point boundary value problem of the type x f t x x t i 0 1 x 0 0 x 1 x 0 1 0 1 the growth of f with respect to x is allowed to be quadratic we use some degree theory arguments to get the multiplicity result

a discontinuous galerkin finite element method for dynamic and wave propagation problems in non linear solids and saturated porous media a time discontinuous galerkin finite element method dgfem for dynamics and wave propagation in non linear solids and saturated porous media is presented the main distinct characteristic of the proposed dgfem is that the specific p3 p1 interpolation approximation which uses piecewise cubic hermite s polynomial and linear interpolations for both displacements and velocities in the time domain is particularly proposed consequently continuity of the displacement vector at each discrete time instant is exactly ensured whereas discontinuity of the velocity vector at the discrete time levels still remains the computational cost is then obviously saved particularly in the materially non linear problems as compared with that required for the existing dgfem both the implicit and explicit algorithms are developed to solve the derived formulations for linear and materially non linear problems numerical results illustrate good performance of the present method in eliminating spurious numerical oscillations and in providing much more accurate solutions over the traditional galerkin finite element method using the newmark algorithm in the time domain copyright 2003 john wiley sons ltd

performance of digital linear modulations on weibull slow fading channels a closed form expression is derived for the moment generating function of the weibull distribution valid when its fading parameter assumes integer values expressions for average signal to noise ratio signal outage and average symbol error rate are derived for single channel reception and independent multichannel diversity reception operating on flat weibull slow fading channels

an unconditionally stable algorithm for generalized thermoelasticity based on operator splitting and time discontinuous galerkin finite element methods an efficient time stepping algorithm is proposed based on operator splitting and the space time discontinuous galerkin finite element method for problems in the non classical theory of thermoelasticity the non classical theory incorporates three models the classical theory based on fourier s law of heat conduction resulting in a hyperbolic parabolic coupled system a non classical theory of a fully hyperbolic extension and a combination of the two the general problem is split into two contractive sub problems namely the mechanical phase and the thermal phase each sub problem is discretized using the space time discontinuous galerkin finite element method the sub problems are stable which then leads to unconditional stability of the global product algorithm a number of numerical examples are presented to demonstrate the performance and capability of the method

a generalized upper and lower solutions method and multiplicity results for nonlinear first order ordinary differential equations abstract we introduce a generalized upper and lower solutions method for the solvability of first order ordinary differential equations u t t u t u 0 u 1 in order to cover the case when the function satisfies caratheodory conditions this method is then applied to get multiplicity results when the nonlinearity interacts with the real eigenvalue of the linearized problem our proofs are based on differential inequalities and classical leray schauder degree

adaptive spacetime method using riemann jump conditions for coupled atomistic continuum dynamics abstract we combine the spacetime discontinuous galerkin sdg method for elastodynamics with the mathematically consistent atomistic discontinuous galerkin adg method in a new scheme that concurrently couples continuum and atomistic models of dynamic response in solids the formulation couples non overlapping continuum and atomistic models across sharp interfaces by weakly enforcing jump conditions for both momentum balance and kinematic compatibility using riemann values to preserve the characteristic structure of the underlying hyperbolic system momentum balances to within machine precision accuracy over every element on each atom and over the coupled system with small controllable energy dissipation in the continuum region that ensures numerical stability when implemented on suitable unstructured spacetime grids the continuum sdg model offers linear computational complexity in the number of elements and powerful adaptive analysis capabilities that readily bridge between atomic and continuum scales in both space and time a special trace operator for the atomic velocities and an associated atomistic traction field enter the jump conditions at the coupling interface the trace operator depends on parameters that specify at the scale of the atomic spacing the position of the coupling interface relative to the atoms in a key finding we demonstrate that optimizing these parameters suppresses spurious reflections at the coupling interface without the use of non physical damping or special boundary conditions we formulate the implicit sdg adg coupling scheme in up to three spatial dimensions and describe an efficient iterative solution scheme that outperforms common explicit schemes such as the velocity verlet integrator numerical examples in 1 d time and employing both linear and nonlinear potentials demonstrate the performance of the sdg adg method and show how adaptive spacetime meshing reconciles disparate time steps and resolves atomic scale signals in the continuum

unconditionally stable finite difference scheme and iterative solution of 2d microscale heat transport equation abstract a two dimensional time dependent heat transport equation at the microscale is derived a second order finite difference scheme in both time and space is introduced and the unconditional stability of the finite difference scheme is proved a computational procedure is designed to solve the discretized linear system at each time step by using a preconditioned conjugate gradient method numerical results are presented to validate the accuracy of the finite difference scheme and the efficiency of the proposed computational procedure

an element wise locally conservative galerkin lcg method for solving diffusion and convection diffusion problems an element wise locally conservative galerkin lcg method is employed to solve the conservation equations of diffusion and convection diffusion this approach allows the system of simultaneous equations to be solved over each element thus the traditional assembly of elemental contributions into a global matrix system is avoided this simplifies the calculation procedure over the standard global continuous galerkin method in addition to explicitly establishing element wise flux conservation in the lcg method elements are treated as sub domains with weakly imposed neumann boundary conditions the lcg method obtains a continuous and unique nodal solution from the surrounding element contributions via averaging it is also shown in this paper that the proposed lcg method is identical to the standard global galerkin gg method at both steady and unsteady states for an inside node thus the method has all the advantages of the standard gg method while explicitly conserving fluxes over each element several problems of diffusion and convection diffusion are solved on both structured and unstructured grids to demonstrate the accuracy and robustness of the lcg method both linear and quadratic elements are used in the calculations for convection dominated problems petrov galerkin weighting and high order characteristic based temporal schemes have been implemented into the lcg formulation

discontinuous galerkin framework for adaptive solution of parabolic problems non conforming meshes are frequently employed in adaptive analyses and simulations of multi component systems we develop a discontinuous galerkin formulation for the discretization of parabolic problems that weakly enforces continuity across non conforming mesh interfaces a benefit of the dg scheme is that it does not introduce constraint equations and their resulting lagrange multiplier fields as done in mixed and mortar methods the salient features of the formulation are highlighted through an a priori analysis when coupled with a mesh refinement scheme the dg formulation is able to accommodate multiple hanging nodes per element edge and leads to an effective adaptive framework for the analysis of interface evolution problems we demonstrate our approach by analysing the stefan problem of solidification

a unified approach to some two point three point and four point boundary value problems with caratheodory functions this paper deals with boundary value problems formula and formula wherea b 0 0 aandbare given real numbers gis a continuous strictly increasing function withg r r andfis a caratheodory function satisfying a nagumo condition the problems have solutions if and only if there exist a lower solutionxand an upper solutionyandx t y t for alla t b

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

multi field spacetime discontinuous galerkin methods for linearized elastodynamics we extend the single field spacetime discontinuous galerkin sdg method for linearized elastodynamics of abedi et al 1 to multi field versions a three field method in displacement velocity and strain is derived by invoking a bubnov galerkin weighted residuals procedure on the system of spacetime field equations and the corresponding jump conditions a two field formulation in displacement and velocity and the one field displacement formulation of 1 are obtained from the three field model through strong enforcement of kinematic compatibility relations all of these formulations balance linear and angular momentum at the element level and we prove that they are energy dissipative and unconditionally stable as in 1 we implement the sdg models using a causal advancing front meshing procedure that enables a patch by patch solution procedure with linear complexity in the number of spacetime elements numerical results show that the three field formulation is most efficient wherein all interpolated fields converge at the optimal o hp 1 rate for a given mesh size the three field model delivers error values that are more than an order of magnitude smaller than those of the one and two field models the three field formulation s efficiency is also superior independent of whether the comparison is based on matching polynomial orders or matching convergence rates

performance analysis of dual selection diversity in correlated weibull fading channels ascertaining the importance of the dual selection combining sc receivers and the suitability of the weibull model to describe mobile fading channels we study the performance of a dual sc receiver over correlated weibull fading channels with arbitrary parameters exact closed form expressions are derived for the probability density function the cumulative distribution function and the moments of the output signal to noise ratio snr important performance criteria such as average output snr amount of fading outage probability and average bit error probability for several modulation schemes are studied furthermore for these performance criteria novel closed form analytical expressions are derived the proposed analysis is complemented by various performance evaluation results including the effects of the input snr s unbalancing fading severity and fading correlation on the overall system s performance computer simulation results have verified the validity and accuracy of the proposed analysis

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

adaptive spacetime discontinuous galerkin method for hyperbolic advection diffusion with a non negativity constraint summary applications where the diffusive and advective time scales are of similar order give rise to advection diffusion phenomena that are inconsistent with the predictions of parabolic fickian diffusion models non fickian diffusion relations can capture these phenomena and remedy the paradox of infinite propagation speeds in fickian models in this work we implement a modified frame invariant form of cattaneo s hyperbolic diffusion relation within a spacetime discontinuous galerkin advection diffusion model an h adaptive spacetime meshing procedure supports an asynchronous patch by patch solution procedure with linear computational complexity in the number of spacetime elements this localized solver enables the selective application of optimization algorithms in only those patches that require inequality constraints to ensure a non negative concentration solution in contrast to some previous methods we do not modify the numerical fluxes to enforce non negative concentrations thus the element wise conservation properties that are intrinsic to discontinuous galerkin models are defined with respect to physically meaningful riemann fluxes on the element boundaries we present numerical examples that demonstrate the effectiveness of the proposed model and we explore the distinct features of hyperbolic advection diffusion response in subcritical and supercritical flows copyright 2015 john wiley sons ltd

a tent pitching scheme motivated by friedrichs theory certain friedrichs systems can be posed on hilbert spaces normed with a graph norm functions in such spaces arising from advective problems are found to have traces with a weak continuity property at points where the inflow and outflow boundaries meet motivated by this continuity property an explicit space time finite element scheme of the tent pitching type with spaces that conform to the continuity property is designed numerical results for a model one dimensional wave propagation problem are presented

existence of multiple solutions for some nonlinear boundary value problems abstract by imposing one sided conditions on the nonlinearity where neither regularity nor uniformity is required we prove the existence of either a nonnegative or a nonpositive solution for first and second order ordinary differential equations with periodic neumann or dirichlet boundary conditions positone and nonpositone problems are considered some nonexistence results are also obtained when using generalized ambrosetti prodi type conditions we get the existence of nonnegative and nonpositive solutions for first and second order periodic or neumann boundary value problems our method of proof makes use of topological degree arguments in cones

upper and lower solutions and topological degree this paper deals with second order nonlinear boundary value problems we suppose the existence of upper and lower solutions of the problems which are well ordered i e the lower solution is less than the upper one and we also consider the case of upper and lower solutions having the opposite ordering we prove the relation between the topological degree and strict upper and lower solutions in both cases and using this we get the existence and multiplicity results for the boundary value problems under consideration

an analysis of the discontinuous galerkin method for a scalar hyperbolic equation we prove lp stability and error estimates for the discontinuous galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain using finite element analysis techniques we obtain l2 estimates that are valid on an arbitrary locally regular triangulation of the domain and for an arbitrary degree of polynomials lp estimates for p 2 are restricted to either a uniform or piecewise uniform triangulation and to polynomials of not higher than first degree the latter estimates are proved by combining finite difference and finite element analysis techniques

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

numerical simulation of axisymmetric viscous flows by means of a particle method a vortex particle method for the simulation of axisymmetric viscous flow is presented the flow is assumed to be laminar and incompressible the navier stokes equations are expressed in an integral velocity vorticity formulation the inviscid scheme is based on nitsche s method for axisymmetric vortex sheets meanwhile two techniques are proposed for dealing with the viscous term the first uses an integral green s function method while the second is based on a diffusion velocity approach both are obtained by extension of existing methods for 2d flows the problem of satisfying boundary conditions along the axis of symmetry is specifically addressed the problem is solved by using cut off functions that are derived from the green s function of the axisymmetric diffusion equation the scheme is applied to simulate the evolution of vortex rings at intermediate reynolds number the processes of entrainment and wake formation are evident in the calculations as well as the extension of the support of vorticity due to viscous diffusion

discontinuous galerkin finite element in time for solving periodic differential equations the dynamics of rotating systems can be modeled by ordinary differential equations with periodic time varying coefficients and forcing discontinuous galerkin dg methods which are known to be higher order accurate a stable and locally conservative are used to solve such equations in this work dg methods are shown to find the steady state periodic solution of a constant coefficient structural dynamics problem with periodic forcing and b helicopter rotor rigid blade flapping equation which is a parametric ordinary differential equation with periodic time varying coefficients and periodic forcing convergence of the numerical solution obtained is studied for both the above equations while h and p are refined separately it is found that the dg method works well for these problems and allows the development of an element level error estimate which can be used to monitor convergence and hence develop adaptive schemes it is clear from the results that even though higher order polynomials result in much faster convergence with reduced computational effort it also results in deterioration of the numerical performance for p 12 two adaptive strategies based on the element level displacement jump norm i e h and hp refinement are proposed and demonstrated on problems with higher harmonic forcing primary controls and parametric variations

riemann solutions and spacetime discontinuous galerkin method for linear elastodynamic contact abstract we derive riemann solutions for stick slip and separation contact modes in a linear elastic material with an isotropic coulomb friction relation and explore their numerical implementation the riemann solutions preserve the characteristic structure of the underlying elastodynamic system and imply dynamic contact conditions that are distinct from the quasi static conditions used in some numerical models nonphysical discontinuities in the standard coulomb model at stick slip transitions can cause contact mode chatter in numerical simulations we restate the coulomb relation to remove these artificial discontinuities and eliminate the need for algorithmic remedies discontinuous response at abrupt separation to contact transitions is physically reasonable and we propose a regularization scheme to address this case we implement the riemann contact solutions within an adaptive spacetime discontinuous galerkin sdg code and report numerical results that demonstrate the model s efficacy

the lower bounds of t periodic solutions for the forced duffing equation abstract this paper is devoted to the discussion of the number of t periodic solutions for the forced duffing equation x kx g t x s 1 h t with g t x being a continuous function by using the degree theory upper and lower solutions method and the twisting theorem

a spacetime discontinuous galerkin method for scalar conservation laws abstract we present a spacetime discontinuous galerkin sdg finite element method for scalar hyperbolic conservation laws the method is consistent with the integral forms of the conservation law and its associated entropy condition written in terms of the physical godunov flux on each spacetime element the discrete basis functions are piecewise continuous in spacetime admitting discontinuities across element boundaries the resulting bubnov galerkin method is high order stable for both convex and non convex flux functions it does not require stabilization beyond the basic galerkin projection the sdg method is applicable to both layered and unstructured spacetime grids an element by element solution scheme delivers o n computational complexity where n is the number of elements when applied to spacetime meshes that conform to a special causality constraint we employ two different limiters to control the local overshoot and undershoot that the basic sdg projection generates near shocks

a spacetime discontinuous galerkin method for hyperbolic heat conduction non fourier conduction models remedy the paradox of infinite signal speed in the traditional parabolic heat equation for applications involving very short length or time scales hyperbolic conduction models better represent the physical thermal transport processes this paper reviews the maxwell cattaneo vernotte modification of the fourier conduction law and describes its implementation within a spacetime discontinuous galerkin sdg finite element method that admits jumps in the primary variables across element boundaries with arbitrary orientation in space and time a causal advancing front meshing procedure enables a patch wise solution procedure with linear complexity in the number of spacetime elements an h adaptive scheme and a special sdg shock capturing operator accurately resolve sharp solution features in both space and time numerical results for one spatial dimension demonstrate the convergence properties of the sdg method as well as the effectiveness of the shock capturing method simulations in two spatial dimensions demonstrate the proposed method s ability to accurately resolve continuous and discontinuous thermal waves in problems where rapid and localized heating of the conducting medium takes place

existence and multiplicity of solutions for four point boundary value problems at resonance abstract this paper deals with the second order four point boundary value problem x t f t x t 0 t 1 x 0 ax x 1 bx where f 0 1 r r is continuous 0 1 0 a 1 1 0 b 1 a 1 b 1 a s 1 b 0 by using the coincidence degree theory the method of lower and upper solutions is established as applications some existence and multiplicity results are obtained

a multiplicity result for a nonlinear boundary value problem abstract in this paper we establish existence and multiplicity results for the problemx x f t x x s t a e in 0 x 0 x under the ambrosetti prodi type condition withfbeing a caratheodory function

a space time discontinuous galerkin method for linearized elastodynamics with element wise momentum balance abstract we present a new space time discontinuous galerkin finite element method for linearized elastodynamics that delivers exact balance of linear and angular momentum over every space time element the method is formulated for use with fully unstructured space time grids and uses displacement basis functions that are discontinuous across all inter element boundaries we introduce a new space time formulation of continuum elastodynamics that uses differential forms and the exterior calculus on manifolds to generate a system of space time field equations and jump conditions then we invoke a bubnov galerkin weighted residuals procedure to formulate the finite element method we describe an implementation on patch wise causal meshes that features linear complexity in the number of elements and special per pixel accurate visualization numerical examples confirm an a priori error estimate and demonstrate the method s shock capturing capabilities

regular article a discontinuous galerkin ale method for compressible viscous flows in moving domains we present a matrix free discontinuous galerkin method for simulating compressible viscous flows in two and three dimensional moving domains to this end we solve the navier stokes equations in an arbitrary lagrangian eulerian ale framework spatial discretization is based on standard structured and unstructured grids but using an orthogonal hierarchical spectral basis the method is third order accurate in time and converges exponentially fast in space for smooth solutions a novelty of the method is the use of a force directed algorithm from graph theory that requires no matrix inversion to efficiently update the grid while minimizing distortions we present several simulations using the new method including validation with published results from a pitching airfoil and new results for flow past a three dimensional wing subject to large flapping insect like motion

a discontinuoushpfinite element method for diffusion problems we present an extension of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems the method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries within each element arbitrary spectral approximations can be constructed with different orderspin each element we demonstrate that the method is elementwise conservative a property uncharacteristic of high order finite elements for clarity we focus on a model class of linear second order boundary value problems and we developpriorierror estimates convergence proofs and stability estimates the results of numerical experiments onh andp convergence rates for representative two dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence

existence and multiplicity results for some three point boundary value problems abstract using the method of upper and lower solutions and some degree theory arguments we establish the existence of at least three solutions of some second order nonlinear differential equations of the type x f t x x t i 0 1 subject to nonlinear three point boundary conditions x 0 0 x 1 g x 0 1 the growth of f with respect to x is allowed to be quadratic

triple positive solutions for nonlinear boundary value problems in banach space in this paper by applying two pairs of lower and upper solutions method and the topological degree theory of strict set contractions the existence of at least three positive solutions to m point boundary value problems for second order ordinary differential equations in banach spaces is obtained

existence of at least three solutions of nonlinear three point boundary value problems with super quadratic growth abstract we establish the existence of at least three solutions in the presence of two lower and two upper solutions of some second order nonlinear three point boundary value problem of the type x f t x x 0 t 1 x 0 0 x 1 x 0 1 0 1 we employ a condition weaker than the well known nagumo condition which allows the nonlinearity f t x x to grow faster than quadratically with respect to x in some cases our method uses some degree theory arguments

numerical analysis of growing crack problems using particle discretization scheme this paper presents the particle discretization scheme pds to analyze brittle failure of solids the scheme uses characteristic functions of voronoi and delaunay tessellations to discretize a function and its derivatives respectively a discretized function has numerous discontinuities so that these discontinuities are utilized as a candidate of crack path segment in modeling propagating cracks without making any extra computation to accommodate new displacement discontinuities when the scheme is implemented to a finite element method fem the resulting stiffness matrix coincides with the one that is obtained by using linear elements the accuracy of computing a stress intensity factor at a crack tip is examined it is shown that the accuracy is better than that of a fem with linear elements when the rotational degree of freedom is included in discretizing displacement functions three three dimensional growing crack problems are solved by means of the pds and the results are presented copyright 2009 john wiley sons ltd

performance of dual maximal ratio combining diversity in nonidentical correlated weibull fading channels using pade spl acute approximation in this letter we evaluate the performance of the dual branch maximal ratio combining mrc diversity scheme in nonidentical correlated weibull fading channels with arbitrary parameters we first use the pade spl acute approximation pa to find closed form rational expressions for the moment generating function mgf of the output signal to noise ratio snr of the mrc receiver different performance measures such as the outage probability and the average symbol error rate for different linear modulations are then presented using the well known mgf approach furthermore the effect of the input snrs unbalancing the severity of fading and the degree of correlation on the system performance are also studied our results are validated by comparing them with computer simulations and we show that the pa technique is indeed a convenient tool for such performance evaluation studies

multiplicity of sign changing solutions for some four point boundary value problem abstract in this paper we obtain using leray schauder degree theory some multiplicity results for sign changing solutions of a four point boundary value problem we assume the existence of a pair of strict lower and upper solutions and some additional conditions on the nonlinear term f

existence and approximation of solutions of second order nonlinear four point boundary value problems abstract we study some four point boundary value problems we use the method of upper and lower solutions to improve some previous existence results and apply the generalized method of quasilinearization to obtain a monotone sequence of iterates converging uniformly and rapidly to a solution of the problem

error estimates for the discontinuous galerkin methods for parabolic equations the classical discontinuous galerkin method for a general parabolic equation is analyzed symmetric error estimates for schemes of arbitrary order are presented the ideas developed below relax many assumptions required in previous work for example different discrete spaces may be used at each time step and the spatial operator need not be self adjoint or independent of time our error estimates are posed in terms of projections of the exact solution onto the discrete spaces and are valid under the minimal regularity guaranteed by the natural energy estimate these projections are local and enjoy optimal approximation properties when the solution is sufficiently regular