canonical forms for linear differential algebraic equations with variable coefficients abstract we give a new set of local characterizing quantities for the treatment of linear differential algebraic equations with variable coefficients this leads to new global invariances under which we can find a generalization of the global or differentiation index and get a new existence and uniqueness theorem

vanishing of categorical obstructions for permutation orbifolds the orbifold construction a mapsto a g for a finite group g is fundamental in rational conformal field theory the construction of rep ag from rep a on the categorical level often called gauging is also prominent in the study of topological phases of matter given a non degenerate braided fusion category mathcal c with a g action the key step in this construction is to find a braided g crossed extension compatible with the action the extension theory of etingof nikshych ostrik gives two obstructions for this problem o 3 in h 3 g and o 4 in h 4 g for certain coefficients the latter of which depends on a categorical lifting of the action and is notoriously difficult to compute we show that in the case where g le s n acts by permutations on mathcal c boxtimes n both of these obstructions vanish this verifies a conjecture of muger and constitutes a nontrivial test of the conjecture that all modular tensor categories come from vertex operator algebras or conformal nets

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

a stabilized mixed finite element method for darcy flow we develop new stabilized mixed finite element methods for darcy flow stability and an a priori error estimate in the stability norm are established a wide variety of convergent finite elements present themselves unlike the classical galerkin formulation which requires highly specialized elements an interesting feature of the formulation is that there are no mesh dependent parameters numerical tests confirm the theoretical results 2002 elsevier science b v all rights reserved

numerical solution of a class of fractional order integro differential algebraic equations using muntz jacobi tau method abstract this paper presents a spectral tau method based on muntz jacobi basis functions for approximating the solutions of fractional order volterra integro differential algebraic equations we examine the solvability of the considered equation and we show that the exact solutions suffer from a singularity at the origin numerical solvability and convergence analysis of the proposed approximate approach are also studied and the error bounds are obtained in a weighted l 2 norm some illustrative examples are presented to validate the theoretical results

a multiscale stabilized finite element method for the advection diffusion equation this paper presents a multiscale method that yields a stabilized finite element formulation for the advection diffusion equation the multiscale method arises from a decomposition of the scalar field into coarse resolved scale and fine unresolved scale the resulting stabilized formulation possesses superior properties like that of the supg and the gls methods a significant feature of the present method is that the definition of the stabilization term appears naturally and therefore the formulation is free of any user designed or user defined parameters another important ingredient is that since the method is residual based it satisfies consistency ab initio based on the proposed formulation a family of 2 d elements comprising 3 and 6 node triangles and 4 and 9 node quadrilaterals has been developed numerical results show the good performance of the method on uniform skewed as well as composite meshes and confirm convergence at optimal rates 2004 elsevier b v all rights reserved

index concepts for linear mixed systems of differential algebraic and hyperbolic type equations for many technical systems the use of a refined network modeling approach leads to hyperbolic type initial boundary value problems of partial differential algebraic equations pdaes the boundary conditions of these systems are governed by time dependent differential algebraic equations daes that couple the pdae system with the network elements that are modeled by daes in time only in order to classify these systems we extend some index notions that have already been introduced to treat parabolic type problems a perturbation index is considered that reflects the sensitivity of the mixed system to slight perturbations in the right hand side of the pdaes as well as in the input signals of the dae systems and initial values in order to make an a posteriori analysis of semidiscretization in space and time we introduce additionally a space and a method of lines mol index here one is especially interested in whether the semidiscretized systems properly reflect the properties of the underlying systems we will show that these indices may detect an artificial sensitivity with respect to perturbations e g if the semidiscretization does not consider the information transport along the characteristics

stability of semidiscrete formulations for parabolic problems at small time steps solutions of direct time integration schemes that converge in time to conventional semidiscrete formulations may be polluted at small time steps by spurious spatial oscillations along with attendant overshoot in time this degradation is not an artifact of the time marching scheme but rather a property of the solution of the semidiscrete formulation itself a critical time step for the onset of spatial oscillations is derived by analogy to singularly perturbed elliptic problems we then propose a simple procedure of spatial stabilization to remove this pathology from implicit time integration schemes without affecting unconditional temporal stability spatially stabilized implicit time integration is free of spurious spatial oscillations at small time steps and numerical experience points to improved temporal accuracy as well

computing reactive flows with a field monte carlo formulation and multi scale methods two novel techniques are merged together to compute efficiently flows involving chemical reaction or combustion in order to predict the evolution of the reacting flow a probability density function approach is applied to the chemical species which is described by a set of pure eulerian transport equations with stochastic source terms the proposed model which has been extended in this case to a multi scalar situation has the advantage that the chemistry terms are closed requiring no modeling the formulation is solved by a stabilized finite element method based on the variational multi scale theory which enables an accurate and stable treatment of the difficult and stiff source terms employing iterative techniques the combination of these ingredients results in a robust and accurate tool for the computation of reactive flows as will be shown in the numerical examples

stabilized methods and post processing techniques for miscible displacements abstract stabilized finite element formulations and post processing techniques are presented for darcy flow and miscible displacement problems in these techniques all primary unknowns are approximated in space by standard equal order interpolations we presented a review of the main mathematical results including convergence estimates for global post processing to solve the pressure velocity problem and for the stabilized solution of the complete set of coupled partial differential equations in both space time and semi discrete frameworks demonstration problems are solved to show that we obtained numerically high rates of convergence than those predicted achieving good accuracy in the solution of monophasic flow problems in adverse conditions

operational tau method for singular system of volterra integro differential equations the legendre spectral tau matrix formulation is proposed to approximate solution of singular system of volterra integro differential equations the existence and uniqueness solution of this system are investigated by means of the smoothing property of a volterra integral operator and some projectors the l 2 convergence of the numerical method is analyzed it is proved theoretically and demonstrated numerically that the proposed method converges exponentially finally two numerical examples illustrate the theoretical results

the semi explicit volterra integral algebraic equations with weakly singular kernels the numerical treatments this paper deals with some theoretical and numerical results for volterra integral algebraic equations iaes of index 1 with weakly singular kernels this type of equations typically has solutions whose derivatives are unbounded at the left endpoint of the interval of integration for overcoming this non smooth behavior of solutions using the appropriate coordinate transformation the primary system is changed into a new iaes which its solutions have better regularity an effective numerical method based on the chebyshev collocation scheme is designed and its convergence analysis is provided our numerical experiments show that the theoretical results are in good accordance with actual convergence rates obtained by the given algorithm

edge stabilization for galerkin approximations of convection diffusion reaction problems n this paper we recall a stabilization technique for finite element methods for convection diffusion reaction equations originally proposed by j douglas jr and t dupont in computing methods in applied sciences second internat sympos versailles 1975 207 216 lecture notes in phys 58 springer berlin 1976 mr0440955 55 13823 the method uses least square stabilization of the gradient jumps across element boundaries we prove that the method is stable in the hyperbolic limit and prove optimal a priori error estimates we address the question of monotonicity of discrete solutions and present some numerical examples illustrating the theoretical results

a variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshes application to vortex shedding the variational multiscale formulation of large eddy simulations developed by hughes and his co workers for incompressible turbulent flows is first extended to the case of compressible turbulent flows next a finite volume element discretization on tetrahedral meshes of this method is proposed this discretization features an economical procedure based on agglomeration for separating a priori the scales a corresponding projector for eliminating the small scales from the system of equations and an effective control of the numerical dissipation induced by upwinding the resulting les method is validated with the three dimensional numerical simulation of a low speed flow past a square cylinder at m 0 1 and re 22 000 and various comparisons with experimental data

the numerical solution of the semi explicit idaes by discontinuous piecewise polynomial approximation abstract in this paper we consider a semi explicit form of volterra integro differential algebraic equations idaes and investigate the existence and uniqueness of solution of these systems by using differentiability index numerical method based on discontinuous piecewise polynomial approximation is proposed for the solution of the semi explicit idaes and global convergence results are established the performance of the numerical scheme is illustrated by means of some test problems

a feti based domain decomposition technique for time dependent first order systems based on a dae approach we present a novel partitioned coupling algorithm to solve first order time dependent non linear problems e g transient heat conduction the spatial domain is partitioned into a set of totally disconnected subdomains the continuity conditions at the interface are modeled using a dual schur formulation where the lagrange multipliers represent the interface fluxes or the reaction forces that are required to maintain the continuity conditions the interface equations along with the subdomain equations lead to a system of differential algebraic equations daes for the resulting equations a numerical algorithm is developed which includes choosing appropriate constraint stabilization techniques the algorithm first solves for the interface lagrange multipliers which are subsequently used to advance the solution in the subdomains the proposed coupling algorithm enables arbitrary numeric schemes to be coupled with different time steps i e it allows subcycling in each subdomain this implies that existing software and numerical techniques can be used to solve each subdomain separately the coupling algorithm can also be applied to multiple subdomains and is suitable for parallel computers we present examples showing the feasibility of the proposed coupling algorithm copyright 2008 john wiley sons ltd

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

approximation of the incompressible navier stokes equations using orthogonal subscale stabilization and pressure segregation on anisotropic finite element meshes abstract this paper describes a finite element model to solve the incompressible navier stokes equations based on the stabilization with orthogonal subscales and a pressure segregation the former consists of adding a least square form of the component orthogonal to the finite element space of the convective and pressure gradient terms this allows to deal with convection dominated flows and to use equal velocity pressure interpolation the pressure segregation is inspired in fractional step schemes although the converged solution corresponds to that of a monolithic time integration likewise we put special emphasis on the use of anisotropic grids in particular we describe some possible choices for the calculation of the element length that appears in the stabilization parameters and check their behavior in two classical numerical examples the preconditioning strategy used to solve the resulting algebraic system for very anisotropic meshes is also briefly described

on gauging symmetry of modular categories topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular tensor category umc a group symmetry of the topological phase induces a group symmetry of its corresponding umc gauging is a well known theoretical tool to promote a global symmetry to a local gauge symmetry we give a mathematical formulation of gauging in terms of higher category formalism roughly given a umc with a symmetry group g gauging is a 2 step process first extend the umc to a g crossed braided fusion category and then take the equivariantization of the resulting category gauging can tell whether or not two enriched topological phases of matter are different and also provides a way to construct new umcs out of old ones we derive a formula for the h 4 obstruction prove some properties of gauging and carry out gauging for two concrete examples

the numerical solution of integral algebraic equations of index 1 by polynomial spline collocation methods in this paper we study polynomial spline collocation methods applied to a particular class of integral algebraic equations of volterra type we analyse mixed systems of second and first kind integral equations global convergence and local superconvergence results are established

pressure bubbles stabilization features in the stokes problem abstract the standard finite element approximation using equal order linear continuous velocity pressure variables is enriched with velocity and pressure bubble functions to model the stokes problem we show by static condensation that these bubble functions give rise to a stabilized method involving least squares forms of the momentum and of the continuity equations in particular pressure bubbles play a key role in explaining the addition of the least squares form of the continuity equation in a stabilized method for stokes

on multi time step monolithic coupling algorithms for elastodynamics we present a way of constructing multi time step monolithic coupling methods for elastodynamics the governing equations for constrained multiple subdomains are written in dual schur form and the continuity of velocities is enforced at system time levels the resulting equations will be in the form of differential algebraic equations to crystallize the ideas we shall employ newmark family of time stepping schemes the proposed method can handle multiple subdomains and allows different time steps as well as different time stepping schemes from the newmark family in different subdomains we shall use the energy method to assess the numerical stability and quantify the influence of perturbations under the proposed coupling method two different notions of energy preservation are introduced and employed to assess the performance of the proposed method several numerical examples are presented to illustrate the accuracy and stability properties of the proposed method we shall also compare the proposed multi time step coupling method with some other methods available in the literature

a three level finite element method for the instationary incompressible navier stokes equations we present a two and a three level finite element method for the numerical simulation of incompressible flow governed by the navier stokes equations within the theoretical framework of the variational multiscale method and exploiting the concept of residual free bubbles we propose a separation of three different scale groups namely large resolved scales small resolved scales and unresolved scales the resolution of the large and small scales takes place on levels 1 and 2 with the aid of diverse approaches the dynamic calculation of a subgrid viscosity representing the effect of the unresolved scales constitutes level 3 of our algorithm the proposed algorithm is tested for various laminar flow situations and compared to the results obtained via an unusual stabilized finite element method it is supposed to be the basic scheme also for turbulent flow in a subsequent study

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

stabilization mechanisms in discontinuous galerkin finite element methods in this paper we propose a new general framework for dg methods which allows to uncover a basic mechanism that ensures suitable stability properties of the methods we show that such a mechanism is essentially the same for apparently unrelated stabilizations such as jump penalty upwinding and hughes franca type residual based stabilizations

coupled discontinuous and continuous galerkin finite element methods for the depth integrated shallow water equations abstract in this paper we investigate a new approach for the two dimensional fully non linear depth averaged shallow water equations by coupling continuous and discontinuous galerkin methods we apply a discontinuous galerkin method to the primitive continuity and momentum equations and couple this to a continuous method discretizing the so called wave continuity and momentum equation herein we present the formulation and derive an a priori error estimate and demonstrate some preliminary numerical results this work represents the culmination of a series of papers exploring coupled methods for the shallow water equations

numerical validation of a class of mixed discontinuous galerkin methods for darcy flow we present a thorough set of numerical experiments to confirm the robustness of several discontinuous galerkin methods proposed for the approximation of darcy law we perform two and three dimensional tests involving both low and high order approximations on cartesian grids and on triangular grids the tests we present confirm the theoretical estimates for symmetric approximations and characterize the behavior of non symmetric approximations where convergence rates that are one order better than predicted are observed for suitable choices of approximation spaces robustness and accuracy of all these methods are assessed for realistic numerical experiments where discontinuous permeability coefficients and bounded smooth permeability functions are used

a discontinuous galerkin method with lagrange multipliers for the solution of helmholtz problems in the mid frequency regime we present a discontinuous galerkin method dgm for the solution of the helmholtz equation in the mid frequency regime our approach is based on the discontinuous enrichment method in which the standard polynomial field is enriched within each finite element by a non conforming field that contains free space solutions of the homogeneous partial differential equation to be solved hence for the helmholtz equation the enrichment field is chosen here as the superposition of plane waves we enforce a weak continuity of these plane waves across the element interfaces by suitable lagrange multipliers preliminary results obtained for two dimensional model problems discretized by uniform meshes reveal that the proposed dgm enables the development of elements that are far more competitive than both the standard linear and the standard quadratic galerkin elements for the discretization of helmholtz problems

a new stabilized finite element formulation for scalar convection diffusion problems the streamline and approximate upwind petrov galerkin method abstract a new stabilized and accurate finite element formulation for convection dominated problems is herein developed the basis of the new formulation is the choice of a new upwind function the upwind function chosen for the new method provokes its degeneration into the supg or cau methods depending on the approximate solution s regularity the accuracy and stability of the new formulation for the linear and scalar advection diffusion equation is demonstrated in several numerical examples

symmetric invariants and cohomology of groups some time ago nakaoka in determined the additive structure of h z f2 around the same time the ring structure of h 274 f2 was calculated and it was assumed that the same type of simple multiplicative relations would appear for n 4 since then most work has concentrated on the embedding 2 o using the polynomial ring structure of h xo f2 in particular most of the recent work in hi was explicitly or implicitly described in m m more than a decade ago and provides no new information on the multiplicative structure of the mod 2 cohomology of finite symmetric groups in this paper we use invariant theory to detect unexpected multiplicative relations in h z f2 the complicated nature of the numerical evidence which we present explains the absence of complete calculations for n 16 the rings of invariants which we study are at the core of any computation of h 2 f2 they build up sucessively yielding relations rich in symmetry but of a highly convoluted type the following problem lies at the heart of all this let p be a polynomial ring k over f2 on n variables and let p k p then ek acts by permuting blocks of generators 1

least squares completions for nonlinear differential algebraic equations a method has been proposed for numerically solving lower dimensional nonlinear higher index differential algebraic equations for which more classical methods such as backward differentiation or implicit runge kutta may not be appropriate this method is based on solving nonlinear dae derivative arrays using nonlinear singular least squares methods the theoretical foundations generality and limitations of this approach remain to be determined this paper carefully examines several key aspects of this approach the emphasis is on general results rather than specific results based on the structure of various applications

differential algebraic equations indices and integral algebraic equations in a recent report hairer lubich and roche report ch 1211 dept de mathematiques universite de geneve geneve switzerland 1988 define the index of differential algebraic equations daes by considering the effect of perturbations of the equations on the solutions this index which will be called the perturbation index p i is one more than the number of derivatives of the perturbation that must appear in any estimate of the bound of the change in the solution an earlier form of index used by a number of authors including gear and petzold siam j numer anal 21 1984 pp 716 728 is determined by the number of differentiations of the daes that are required to generate an ordinary differential equation ode satisfied by the solution this will be called the differential index d i hairer lubich and roche give an example whose differential index is one and perturbation index is two and other examples where they are identical it will be shown that d i leqq p i leqq d i 1 and th

a stabilized mixed discontinuous galerkin method for darcy flow abstract a new mixed stabilized discontinuous galerkin formulation for darcy flow is presented the formulation combines several attributes not simultaneously satisfied by other methods it is convergent for any combination of velocity and pressure interpolation higher than first order it exactly satisfies a mass balance on each element and it passes two and three dimensional constant flow patch tests for distorted element geometries the key ingredient in the formulation is a volumetric residual based stabilization term that does not involve any mesh dependent parameters

optimal convergence results of piecewise polynomial collocation solutions for integral algebraic equations of index 3 in this work we will consider piecewise polynomial collocation methods for a new class of integral algebraic equations of index 3 an analysis of the global convergence properties of the collocation methods is given and the optimal order of convergence results is established the performance of the proposed scheme is illustrated by means of two numerical examples and confirm that we can achieve the expected theoretical orders of convergence

the drazin inverse in multibody system dynamics the numerical analysis of multibody system dynamics is based on the equations of motion as differential algebraic systems a thorough analysis of the linearized equations and their solution theory leads to an equivalent system of ordinary differential equations which gives deeper insight into the derivation of integration schemes and into the stabilization approaches the main tool is the drazin inverse a generalized matrix inverse which preserves the eigenvalues the results are illustrated by a realistic truck model finally the approach is extended to the nonlinear index 2 formulation

a superconvergence result for discontinuous galerkin methods applied to elliptic problems this paper presents a theoretical and numerical study of a class of discontinuous galerkin methods that shows the approximation of the gradient superconverges at the zeros of the legendre polynomials on a model 1d elliptic problem numerical experiments validate the theoretical results

energy norm a posteriori error estimation for discontinuous galerkin methods in this paper we present a residual based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous galerkin approximations of elliptic problems the theory is developed for an elliptic model problem in two and three spatial dimensions and general nonconvex polygonal domains are allowed we also present some illustrating numerical examples

local discontinuous galerkin methods for nonlinear dispersive equations we develop local discontinuous galerkin dg methods for solving nonlinear dispersive partial differential equations that have compactly supported traveling waves solutions the so called compactons the schemes we present extend the previous works of yan and shu on approximating solutions for linear dispersive equations and for certain kdv type equations we present two classes of dg methods for approximating solutions of such pdes first we generate nonlinearly stable numerical schemes with a stability condition that is induced from a conservation law of the pde an alternative approach is based on constructing linearly stable schemes i e schemes that are linearly stable to small perturbations the numerical simulations we present verify the desired properties of the methods including their expected order of accuracy in particular we demonstrate the potential advantages of using dg methods over pseudospectral methods in situations where discontinuous fronts and rapid oscillations co exist in a solution

integral algebraic equations theory of collocation methods i our analysis of collocation solutions for general systems of linear integral algebraic equations iaes is based on the notions of the tractability index and the nu smoothing property of a volterra integral operator these are used to decouple the given iae system into the inherent system of regular second kind volterra integral equations vies and a system of first kind vies this decoupling is then used to derive the optimal convergence properties of piecewise polynomial collocation solutions numerical examples illustrate the theoretical results

discontinuous continuous galerkin methods for coupling the primitive and wave continuity equations of shallow water in this paper we investigate a new approach for the numerical solution of the two dimensional depth integrated shallow water equations based on coupling discontinuous and continuous galerkin methods in this approach we couple a discontinuous galerkin method applied to the primitive continuity equation coupled to a continuous galerkin method applied to the so called wave continuity equation the formulation is derived and a priori error estimates are given preliminary numerical results for a simple model of flow in a channel are presented 2003 elsevier b v all rights reserved

combinatorial relaxation algorithm for mixed polynomial matrices the notion of mixed polynomial matrices is a mathematical tool for faithful description of discrete physical engineering dynamical systems it distinguishes two kinds of numbers fixed constants that account for conservation laws and independent parameters that represent physical characteristics

a discontinuous galerkin formulation for a strain gradient dependent damage model abstract the numerical solution of strain gradient dependent continuum problems has been dogged by continuity demands on the basis functions for most commonly accepted models solutions using the finite element method demand c 1 continuity of the shape functions here recent developments in discontinuous galerkin methods are explored and exploited for the solution of a prototype non linear strain gradient dependent continuum model a formulation is developed that allows the rigorous solution of a strain gradient damage model using standard c 0 shape functions the formulation is tested in one dimension for the simplest possible finite element formulation continuous piecewise linear displacement and constant on elements internal variable numerical results are shown to compare excellently with a benchmark solution the results are remarkable given the simplicity of the proposed formulation

error analysis of imex runge kutta methods derived from differential algebraic systems in this paper we present an error analysis of the imex runge kutta methods when applied to stiff problems containing a nonstiff term and a stiff term characterized by a small stiffness parameter varepsilon in this analysis we expand the global error in powers of varepsilon and show that the coefficients of the error are the global errors of the imex runge kutta method applied to a differential algebraic system interesting convergence results of these errors and of the remainder of the expansion allow us to determine sharp error bounds for stiff problems as a representative example of stiff problems we have chosen the van der pol equation we illustrate that the theoretical prediction is confirmed by the numerical test specifically an order reduction phenomenon is observed when the problem becomes increasingly stiff in particular making several assumptions we try to improve global error estimates of several imex runge kutta methods existing in the literature

hierarchical high order finite element spaces in h div ω h1 ω for a stabilized mixed formulation of darcy problem abstract the classical dual mixed finite element method for flow simulations is based on h div conforming approximation spaces for the flux which guarantees continuous normal components on element interfaces and discontinuous approximations in l 2 for the pressure however stability and convergence can only be obtained for compatible approximation spaces stabilized finite element methods may provide an alternative stable procedure to avoid this kind of delicate balance the main purpose of this paper is to present a high order finite element methodology to solve the darcy problem based on the combination of an unconditionally stable mixed finite element method with a hierarchical methodology for the construction of finite dimensional subspaces of h div and h 1 the chosen stabilized method is free of mesh dependent stabilization parameters and allows for the use of different high order finite element approximations for the flux and the pressure variables without requiring any compatibility constraint as required in mixed methods for these problems convergence studies are presented comparing the numerical solutions obtained for different approximation orders on quadrilateral elements with the ones given by classical mixed formulation with raviart thomas elements

fusion rules for z 2z permutation gauging in this note we examine the gauging of the z 2z permutation action on the tensor square of a modular tensor category c when c is unpointed we provide formulas for the fusion rules of the gauged category which nontrivially involves the modular data of c our technique highlights the use of generalized frobenius schur indicators we discuss several examples related to quantum groups at roots of unity in this note we examine the gauging of the z 2z permutation action on the tensor square of a modular tensor category c when c is unpointed we provide formulas for the fusion rules of the gauged category which nontrivially involves the modular data of c our technique highlights the use of generalized frobenius schur indicators we discuss several examples related to quantum groups at roots of unity

structural analysis of linear integral algebraic equations abstract the choice of a feasible numerical method for the solution of an integral algebraic equation iae requires knowledge about its index and solvability in this paper the method for structural analysis of differential algebraic equation systems daes is extended to analyze the structure of a linear iae its index and solvability are determined based on the sparsity pattern of the iae and the smoothing property of a volterra integral operator

improving stability and accuracy of reissner mindlin plate finite elements via algebraic subgrid scale stabilization abstract stabilized finite element methods for the solution of reissner mindlin type plate problems are presented the formulations are based on previously described mixed formulations like the assumed natural strain ans or mitc concept or the discrete shear gap dsg method in particular the algebraic subgrid scale asgs formulation is used for the stabilization term the essential idea is to obtain stable elements and improve coarse mesh accuracy at the same time it is shown how this can be achieved by a proper choice of stabilization parameters on the basis of physical insight into the mechanical behavior of shear deformable plates in this context there is a strong relationship to concepts that have been developed long before stabilization techniques appeared in finite element technology particularly the residual bending flexibility or deflection matching technique

the index of general nonlinear daes in the last few years there has been considerable research on differential algebraic equations daes f t y y 0 where f y is identically singular much of the mathematical effort has focused on computing a solution that is assumed to exist more recently there has been some discussion of solvability of daes there has historically been some imprecision in the use of the two key concepts of solvability and index for daes the index is also important in control and systems theory but with different terminology the consideration of increasingly complex nonlinear daes makes a clear and correct development necessary this paper will try to clarify several points concerning the index after establishing some new and more precise terminology that we need some inaccuracies in the literature will be corrected the two types of indices most frequently used the differentiation index and the perturbation index are defined with respect to solutions of unperturbed problems examples are given to show that these indices can be very different for the same problem we define new maximum indices which are the maxima of earlier indices in a neighborhood of the solution over a set of perturbations and show that these indices are simply related to each other these indices are also related to an index defined in terms of jacobians