a new completely general class of variational inclusions with noncompact valued mappings abstract in this paper we introduce and study a new completely general class of variational inclusions with noncompact valued mappings and construct some new iterative algorithms we prove the existence of solutions for the completely general class of variational inclusions and the convergence of iterative sequences generated by the algorithms

three step iterative algorithm for a system of set valued variational inclusions with h η monotone operators abstract in this paper we introduce and study a new system of set valued variational inclusions with h monotone operators we prove the convergence of a new three step iterative algorithm for this system of set valued variational inclusions the results in this paper extend and improve some known results from the literature

factorization of minty and stampacchia variational inequality systems abstract in this paper sufficient regularity and coercivity conditions for minty and stampacchia type variational inequality systems are offered the typical results state that if the independent inequalities are solvable and the functions involved are lower semicontinuous then the system has also a solution that is a factorization principle holds as an application a variational inequality system consisting of two partial differential inequalities is considered this result is analogous to that of chen journal of mathematical analysis and application 231 1999 177 obtained for one variational inequality

parallel space time hp adaptive discretization scheme for parabolic problems abstract we introduce an integration scheme for parabolic problems our parallelizable method uses adaptive h p finite elements in space and finite differences in time the strategy can also be combined with a classical finite element method parallelization technique based on domain decomposition we verified the performance of our method against two different benchmarks in both two dimensional model problem on an l shaped domain and three dimensional pennes bioheat equation settings results show a significant speedup in computational time when compared with the sequential version of the algorithm moreover we develop a mathematical framework to analyze similar schemes which include h p spatial adaptivity our framework describes error propagation rigorously and as such allows to analyze convergence properties of these mixed methods

projection methods algorithms and a new system of nonlinear variational inequalities abstract the convergence of projection methods is based on a new iterative algorithm for the approximation solvability of the following system of nonlinear variational inequalities snvi determine elements x y k such that t y x y x x 0 for all x k and for 0 and t x y x x y 0 for all x k and for 0 where t k h is a mapping from a nonempty closed convex subset k of a real hilbert space h into h this new class of generalized nonlinear variational inequalities reduces to standard class of nonlinear variational inequalities which are widely studied and applied to various problems arising from mathematical sciences optimization and control theory and other related fields

comparison theorem for kahler manifolds and positivity of spectrum the first part of this paper is devoted to proving a comparison theorem for kahler manifolds with holomorphic bisectional curvature bounded from below the model spaces being compared to are m m and m in particular it follows that the bottom of the spectrum for the laplacian is bounded from above by m2 for a complete m dimensional kahler manifold with holomorphic bisectional curvature bounded from below by 1 the second part of the paper is to show that if this upper bound is achieved and when m 2 then it must have at most four ends

co coercivity and its role in the convergence of iterative schemes for solving variational inequalities this paper stresses the role of co coercivity and related notions in the convergence of iterative schemes for solving monotone but not necessarily strongly or even strictly monotone variational inequalities the analysis will be conducted within the conceptual framework of the auxiliary problem principle

asymmetric variational inequality problems over product sets applications and iterative methods in this paper we i describe how several equilibrium problems can be uniformly modelled by a finite dimensional asymmetric variational inequality defined over a cartesian product of sets and ii investigate the local and global convergence of various iterative methods for solving such a variational inequality problem because of the special cartesian product structure these iterative methods decompose the original variational inequality problem into a sequence of simpler variational inequality subproblems in lower dimensions the resulting decomposition schemes often have a natural interpretation as some adjustment processes

the h p and h p versions of the finite element methods in 1 dimension part iii the adaptive h p version abstract the paper is the third and final part in the series of three devoted to the detailed analysis of the three basic versions of the finite element method in one dimension the first part analyzed the p version and the second part concentrated on the h and h p version this paper analyzes a theoretical frame of the adaptive h p version and based on it the authors provide concrete algorithm for the one dimensional problem it is proven that in the case that the solution has x sub alpha type singularity the adaptive algorithm give an exponential rate of convergence very close to the optimal one analyzed in the second part of the paper additional keyword error analysis

hp fem electromechanical transduction model of ionic polymer metal composites we propose a mathematically explicit model of ionic polymer metal composite ipmc materials that consist of a coupled system of poisson nernst planck euler equations discretized by means of adaptive higher order finite element methods hp fem we show that due to the transient character of the problem and different fields in terms of the locations of field gradients in the domain it is efficient to use adaptive algorithms that are capable of changing the mesh dynamically in time we also show that due to large qualitative and quantitative differences between the four solution components cation concentration electric potential x directional displacement and y directional displacement it is efficient to approximate them on different meshes using a novel adaptive multi mesh hp fem the study is accompanied with computations and comparisons of the adaptive multi mesh hp fem with a number of adaptive fem algorithms

complete manifolds with positive spectrum ii in this paper we continued our investigation of complete manifolds whose spectrum of the laplacian has an optimal positive lower bound in particular we proved a splitting type theorem for n dimensional manifolds that have a finite volume end this can be viewed as a study of the equality case of a theorem of cheng

set valued resolvent equations and mixed variational inequalities in this paper we introduce and study a new class of variational inequalities which is called the generalized set valued mixed variational inequality the resolvent operator technique is used to establish the equivalence among generalized set valued variational inequalities fixed point problems and the generalized set valued resolvent equations this equivalence is used to study the existence of a solution of set valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems the results proved in this paper represent a significant refinement and improvement of the previously known results in this area

a new system of variational inclusions with h η monotone operators in hilbert spaces in this paper we introduce and study a new system of variational inclusions involving h h monotone operators in hilbert space using the resolvent operator associated with h h monotone operators we prove the existence and uniqueness of solutions for this new system of variational inclusions we also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm

on the existence and iterative approximation problems of solutions for set valued variational inclusions in banach spaces the purpose of this paper is to introduce and study a class of set valued variational inclusions in banach spaces by using michael s selection theorem and nadler s theorem some existence theorems and iterative algorithms for solving this kind of set valued variational inclusion in banach spaces are established and suggested

multi domain muffin tin finite element density functional calculations for small molecules in this contribution a multi domain finite element density functional code for molecules is presented the method makes use of higher order elements to enforce the continuity of the orbitals between the spherical domains and the interstitial domain the salient computational details of the algorithm are described in some detail results of calculations for the orbital energies of methane ethane water ammonia and benzene are given and compared with those obtained using gpaw

monolithic discretization of linear thermoelasticity problems via adaptive multimesh hp fem in linear thermoelasticity models the temperature t and the displacement components u 1 u 2 exhibit large qualitative differences while t typically is very smooth everywhere in the domain the displacements u 1 u 2 have singular gradients stresses at re entrant corners and edges the mesh must be extremely fine in these areas so that stress intensity factors are resolved sufficiently one of the best available methods for this task is the exponentially convergent hp fem note however that standard adaptive hp fem approximates all three fields u 1 u 2 and t on the same mesh and thus it treats t as if it were singular at re entrant corners as well therefore a large number of degrees of freedom of temperature are wasted this motivates us to approximate the fields u 1 u 2 and t on individual hp meshes equipped with mutually independent hp adaptivity mechanisms in this paper we describe mathematical and algorithmic aspects of the novel adaptive multimesh hp fem and demonstrate numerically that it performs better than the standard adaptive h fem and hp fem

static condensation partial orthogonalization of basis functions and ilu preconditioning in the hp fem static condensation of internal degrees of freedom partial orthogonalization of basis functions and ilu preconditioning are techniques used to facilitate the solution of discrete problems obtained in the hp fem this paper shows that for symmetric linear not necessarily positive definite problems under mild technical assumptions these three techniques are completely equivalent in fact the same matrices can be obtained by the same arithmetic operations the study can be extended to nonsymmetric problems naturally

sensitivity analysis for parametric completely generalized strongly nonlinear implicit quasi variational inclusions in this paper by using a resolvent operator technique of maximal monotone mappings and the property of a fixed point set of set valued contractive mappings we study the behavior and sensitivity of the solutions of the parametric completely generalized strongly nonlinear implicit quasi variational inclusion in hilbert space our results extend improve and unify the previously many results in this field

generalized set valued variational inclusions and resolvent equations in this paper we establish the equivalence between the generalized set valued variational inclusions the resolvent equations and the fixed point problem using the resolvent operator technique this equivalence is used to suggest and analyze some iterative algorithms for solving the generalized set valued variational inclusions and related optimization problems

on the existence of solutions of variational inequalities in banach spaces abstract in this paper we study the existence of the solution of the variational inequality tx y x 0 by applying the generalized projection operator k b b where b is a banach space with dual space b and by using the well known fankkm theorem

iterative algorithm for a system of nonlinear variational like inclusions in this paper we consider a system of nonlinear variational like inclusions snvli in hilbert spaces in particular snvli reduces to a variational inclusion an extension of variational inclusion studied by h a s s o u n i a n d m o u d a f i 1 using fixed point method we suggest an iterative algorithm for finding an approximate solution to snvli further we prove the existence of solution and discuss convergence criteria for the approximate solution of snvli the theorems presented in this paper improve and unify many known results of variational inclusions and variational inequalities see for example 1 3

anisotropic hp mesh optimization technique based on the continuous mesh and error models abstract we develop a new mesh adaptive technique for the numerical solution of partial differential equations pdes using the h p version of the finite element method h p fem the technique uses a combination of approximation and interpolation error estimates to generate anisotropic triangular elements as well as appropriate polynomial approximation degrees we present a h p version of the continuous mesh model as well as the continuous error model which are used for the formulation of a mesh optimization problem solving the optimization problem leads to h p mesh with the smallest number of degrees of freedom under the constraint that the approximate solution has an error estimate below a given tolerance further we propose an iterative algorithm to find a suitable anisotropic h p mesh in the sense of the mesh optimization problem several numerical examples demonstrating the efficiency and applicability of the new method are presented

related aspects of positivity in riemannian geometry pour une variete de riemann on etudie le lien entre le point 0 du l 2 spectre le plus proche de zero pour l extension de friedrich d un operateur semi defini symetrique et le taux exponentiel de transition d un operateur de markoff conservant la positivite

goal oriented hp adaptivity for elliptic problems we propose and test a fully automatic goal oriented hp adaptive strategy for elliptic problems the method combines two techniques the standard goal oriented adaptivity based on a simultaneous solution of a dual problem and a recently proposed hp strategy based on minimizing the projection based interpolation error of a reference solution the proposed strategy is illustrated with two numerical examples laplace equation in l shape domain and an axisymmetric maxwell problem involving radiation of a loop antenna wrapped around a metallic cylinder into a conductive medium

modified resolvent splitting algorithms for general mixed variational inequalities in this paper we suggest and analyze a number of four step resolvent splitting algorithms for solving general mixed variational inequalities by using the updating technique of the solution the convergence of these new methods requires either monotonicity or pseudomonotonicity of the operator proof of convergence is very simple our new methods differ from the existing splitting methods for solving variational inequalities and complementarity problems the new results are versatile and are easy to implement

three step iterative algorithms for multivalued quasi variational inclusions in this paper we suggest and analyze some new classes of three step iterative algorithms for solving multivalued quasi variational inclusions by using the resolvent equations technique new iterative algorithms include the ishikawa mann and noor iterations for solving variational inclusions inequalities and optimization problems as special cases the results obtained in this paper represent an improvement and a significant refinement of previously known results

a sharp estimate for the bottom of the spectrum of the laplacian on kahler manifolds on a complete noncompact kahler manifold we prove that the bottom of the spectrum for the laplacian is bounded from above by m 2 if the ricci curvature is bounded from below by 2 m 1 then we show that if this upper bound is achieved then the manifold has at most two ends these results improve previous results on this subject proved by p li and j wang in l w3 and l w under assumptions on the bisectional curvature

perturbed algorithms and sensitivity analysis for a general class of variational inclusions in the present paper we study a perturbed iterative method for solving a general class of variational inclusions an existence result which generalizes some known results in this field a convergence result and a new iterative method are given we also prove the continuity of the perturbed solution to a parametric variational inclusion problem several special cases are discussed

three anisotropic benchmark problems for adaptive finite element methods in this paper we provide three benchmark problems with known exact solutions that can be used to assess the ability of adaptive finite element algorithms to handle anisotropically behaved solutions the first one is a poisson equation with a smooth solution that only changes in one spatial direction the second one is a singularly perturbed linear elliptic equation whose solution exhibits a boundary layer and the last one is a two equation system that contains a boundary layer in one solution component only in an appendix we show sample results obtained with the open source library hermes http hpfem org hermes

solving a suite of nist benchmark problems for adaptive fem with the hermes library recently a new suite of twelve benchmark problems for adaptive finite element methods fem was published at the us national institute for standards and technology nist these benchmark problems come with exact solutions and they exhibit all typical difficulties associated with elliptic problems including singularities steep internal layers anisotropy and oscillations in this paper we solve these benchmark problems using the open source library hermes http hpfem org all these results are reproducible they are part of the git repository of the open source hermes project and the reader can experiment with them by himself herself instructions for this are provided we hope that authors of other adaptive fem codes will make their results for these test problems available in a reproducible fashion as well

the poisson equation on complete manifolds with positive spectrum and applications abstract in this paper we investigate the existence of a solution to the poisson equation on complete manifolds with positive spectrum and ricci curvature bounded from below we show that if a function f has decay f o r 1 e for some e 0 where r is the distance function to a fixed point then the poisson equation u f has a solution u with at most exponential growth we apply this result on the poisson equation to study the existence of harmonic maps between complete manifolds and also existence of hermitian einstein metrics on holomorphic vector bundles over complete manifolds thus extending some results of li tam and ni assuming moreover that the manifold is simply connected and of ricci curvature between two negative constants we can prove that in fact the poisson equation has a bounded solution and we apply this result to the ricci flow on complete surfaces

h monotone operator and resolvent operator technique for variational inclusions in this paper we introduce a new class of monotone operators h monotone operators the resolvent operator associated with an h monotone operator is defined and its lipschitz continuity is presented we also introduce and study a new class of variational inclusions involving h monotone operators and construct a new algorithm for solving this class of variational inclusions by using the resolvent operator technique

pde independent adaptive hp fem based on hierarchic extension of finite element spaces we present a novel approach to automatic adaptivity in higher order finite element methods hp fem which is free of analytical error estimates this means that a computer code based on this approach can be used to solve adaptively a wide range of pde problems a posteriori error estimation is done computationally via hierarchic extension of finite element spaces this is an analogy to embedded higher order methods for ode the adaptivity process yields a sequence of embedded stiffness matrices which are solved efficiently using a simple combined direct iterative algorithm the methodology works equally well for standard low order fem and for the hp fem numerical examples are presented