solving electromagnetic eigenvalue problems in polyhedral domains with nodal finite elements a few years ago costabel and dauge proposed a variational setting which allows one to solve numerically the time harmonic maxwell equations in 3d polyhedral geometries with the help of a continuous approximation of the electromagnetic field in order to remove spurious eigenmodes their method required a parameterization of the variational formulation in order to avoid this difficulty we use a mixed variational setting instead of the parameterization which allows us to handle the divergence free constraint on the field in a straightforward manner the numerical analysis of the method is carried out and numerical examples are provided to show the efficiency of our approach

on some classes of nonstationary axially symmetric solutions to the navier stokes equations in the paper the navier stokes equations are studied in axially symmetric cases of nonstationary motion with rotation of incompressible viscous fluids the problem is reduced to a nonlinear system of three partial differential equations for three unknown functions of the cylindrical coordinates r and z and time t the three functions are sought in the form of power series in r with coefficients depending on t and z for the unknown coefficients recurrence relations are obtained which contain three arbitrary functions the relations are examined in three particular cases in which they give analytical solutions to the navier stokes equations for any values of the coordinates t z and r

on a particular analytical solution to the 3d navier stokes equations and its peculiarity for high reynolds numbers a special class of axially symmetric nonstationary flows of incompressible viscous fluids is examined for it the 3d navier stokes equations are reduced to a nonlinear partial differential equation of the third order and a linear partial differential equation of the second order these equations are studied and their particular analytical solutions are found the obtained particular solution to the navier stokes equations could be used to describe some types of turbulent flows of viscous fluids in the case of high reynolds numbers

regularity of the maxwell equations in heterogeneous media and lipschitz domains abstract this note establishes regularity estimates for the solution of the maxwell equations in lipschitz domains with non smooth coefficients and minimal regularity assumptions the argumentation relies on elliptic regularity estimates for the poisson problem with non smooth coefficients

mixed finite elements for electromagnetic analysis the occurrence of spurious solutions is a well known limitation of the standard nodal finite element method when applied to electromagnetic problems the two commonly used remedies that are used to address this problem are i the addition of a penalty term with the penalty factor based on the local dielectric constant and which reduces to a helmholtz form on homogeneous domains regularized formulation ii a formulation based on a vector and a scalar potential both these strategies have some shortcomings the penalty method does not completely get rid of the spurious modes and both methods are incapable of predicting singular eigenvalues in non convex domains some non zero spurious eigenvalues are also predicted by these methods on non convex domains in this work we develop mixed finite element formulations which predict the eigenfrequencies including their multiplicities accurately even for nonconvex domains the main feature of the proposed mixed finite element formulation is that no ad hoc terms are added to the formulation as in the penalty formulation and the improvement is achieved purely by an appropriate choice of finite element spaces for the different variables we show that the formulation works even for inhomogeneous domains where double noding is used to enforce the appropriate continuity requirements at an interface for two dimensional problems the shape of the domain can be arbitrary while for the three dimensional ones with our current formulation only regular domains which can be nonconvex can be modeled since eigenfrequencies are modeled accurately these elements also yield accurate results for driven problems c 2014 elsevier ltd all rights reserved

on the helicity in 3d periodic navier stokes equations ii the statistical case we study the asymptotic behavior of the statistical solutions to the navier stokes equations using the normalization map 9 it is then applied to the study of mean energy mean dissipation rate of energy and mean helicity of the spatial periodic flows driven by potential body forces the statistical distribution of the asymptotic beltrami flows are also investigated we connect our mathematical analysis with the empirical theory of decaying turbulence with appropriate mathematically defined ensemble averages the kolmogorov universal features are shown to be transient in time we provide an estimate for the time interval in which those features may still be present our collaborator and friend basil nicolaenko passed away in september of 2007 after this work was completed honoring his contribution and friendship we dedicate this article to him

effects of discontinuous magnetic permeability on magnetodynamic problems a novel approximation technique using lagrange finite elements is proposed to solve magneto dynamics problems involving discontinuous magnetic permeability and non smooth interfaces the algorithm is validated on benchmark problems and is used for kinematic studies of the cadarache von karman sodium 2 vks2 experimental fluid dynamo

nodal finite element de rham complexes we construct 2d and 3d finite element de rham sequences of arbitrary polynomial degrees with extra smoothness some of these elements have nodal degrees of freedom and can be considered as generalisations of scalar hermite and lagrange elements using the nodal values the number of global degrees of freedom is reduced compared with the classical nedelec and brezzi douglas marini finite elements and the basis functions are more canonical and easier to construct our finite elements for h mathrm div with regularity r 2 coincide with the nonstandard elements given by stenberg numer math 115 1 131 139 2010 we show how regularity decreases in the finite element complexes so that they branch into known complexes the standard de rham complexes of whitney forms and their higher order version can be regarded as the family with the lowest regularity the construction of the new families is motivated by finite element systems

exponential averaging for hamiltonian evolution equations we derive estimates on the magnitude of non adiabatic interaction between a hamiltonian partial differential equation and a high frequency nonlinear oscillator assuming spatial analyticity of the initial conditions we show that the dynamics can be transformed to the uncoupled dynamics of an infinite dimensional hamiltonian system and an anharmonic oscillator up to coupling terms which are exponentially small in a certain power of the frequency of the oscillator the result is derived from an abstract averaging theorem for infinite dimensional analytic evolution equations in gevrey spaces refining upon a similar result by neishtadt for analytic ordinary differential equations the temporal estimate crucially depends on the spatial regularity of the initial condition the result shows to what extent the strong resonances between rapid forcing and highly oscillatory spatial modes can be suppressed by the choice of sufficiently smooth initial data an application is provided by a system of nonlinear schrodinger equations coupled to a rapidly forcing single mode representing small scale oscillations we provide an example showing that the estimates for partial differential equations we derive here are necessarily different from those in the context of ordinary differential equations

approximation of the eigenvalue problem for the time harmonic maxwell system by continuous lagrange finite elements we propose and analyze an approximation technique for the maxwell eigenvalue problem using h1 conforming finite elements the key idea consists of considering a mixed method controlling the divergence of the electric field in a fractional sobolev space h with 1 2 1 the method is shown to be convergent and spectrally correct

on a finite element method for solving the three dimensional maxwell equations abstract the aim of this paper is to present a method for solving the time domain three dimensional maxwell equations which can be coupled with a particle solver for this purpose maxwell s equations are reformulated as a constrained wave equation system with lagrange multipliers associated to the conditions 0 and e e 0 we approximate both the fields and the lagrange multipliers with a finite element method using a taylor hood element

a rigorous treatment of experimental observations for the two dimensional navier stokes equations within a fully rigorous framework this paper shows that a finite number of point observations distributed in both space and time serve to determine the fully developed flow of a two dimensional fluid throughout the whole flow domain with the measurements taken at one fixed time the results imply that if the flow is resolved on a sufficiently small scale then its dynamics are entirely determined applied to experimental observations taken randomly from a small neighbourhood of one point in space but at staggered times they imply a version of taken s time delay embedding theorem

edge element methods for maxwell s equations with strong convergence for gauss laws in this paper we propose and investigate some edge element approximations for three maxwell systems in three dimensions the stationary maxwell equations the time harmonic maxwell equations and the time dependent maxwell equations these approximations have three novel features first the resulting discrete edge element systems can be solved by some existing preconditioned solvers with optimal convergence rate independent of nite element meshes including the stationary maxwell equations second they ensure the optimal strong convergence of the gauss laws in some appropriate norm in addition to the standard optimal convergence in energy norm under the general weak regularity assumptions that hold for both convex and non convex polyhedral domains and for the discontinuous coecients that may have large jumps across the interfaces between dierent media finally no saddle point discrete systems are needed to solve for the stationary maxwell equations unlike most existing edge element schemes

mc cdma performance evaluation over a multipath fading channel using the characteristic function method this letter presents an efficient and accurate performance evaluation method for binary mc cdma systems with deterministic signature sequences this method is based on a formulation of the characteristic function and does not resort to any assumption on the statistical or spectral behavior of the interference the accuracy of the gaussian approximation method is also considered

a note on gevrey class regularity for the solutions of the navier stokes equations abstract in this note we present results on gevrey class regularity of the solutions of the navier stokes equations with space periodic boundary conditions we give a generalization of results of c foias and r temam j funct anal 87 359 369 1988

discontinuous galerkin computation of the maxwell eigenvalues on simplicial meshes this paper is concerned with the discontinuous galerkin approximation of the maxwell eigenproblem after reviewing the theory developed in a buffa i perugia discontinuous galerkin approximation of the maxwell eigenproblem technical report 24 pv imati cnr pavia italy 2005 we present a set of numerical experiments which both validate the theory and provide further insight regarding the practical performance of discontinuous galerkin methods particularly in the case when non conforming meshes characterized by the presence of hanging nodes are employed

on the lagrangian and eulerian analyticity for the euler equations abstract we address preservation of the lagrangian analyticity radius of solutions to the euler equations belonging to natural analytic space based on the size of taylor or gevrey coefficients we prove that if the solution belongs to such space then the solution also belongs to it for a positive amount of time we also prove the local analog of this result for a sufficiently large gevrey parameter however we show that the preservation holds independently of the size of the radius finally we construct a solution which shows that the first result does not hold in the eulerian setting

nonsymmetric bifurcations of solutions of the 2d navier stokes system abstract we consider the 2d navier stokes system written for the stream function with periodic boundary conditions and construct a set of initial data such that initial critical points bifurcate from 1 to 2 and then to 3 critical points in finite time the bifurcation takes place in a small neighborhood of the origin our construction does not require any symmetry assumptions or the existence of special fixed points for another set of initial data we show that 3 critical points merge into 1 critical point in finite time we also construct a set of initial data so that bifurcation can be generated by the navier stokes flow and do not require the existence of an initial critical point

local two sided bounds for eigenvalues of self adjoint operators we examine the equivalence between an extension of the lehmann maehly goerisch method developed a few years ago by zimmermann and mertins and a geometrically motivated method developed more recently by davies and plum we establish a general framework which allows sharpening various previously known results in these two settings and determine explicit convergence estimates for both methods we demonstrate the applicability of the method of zimmermann and mertins by means of numerical tests on the resonant cavity problem

a nodal based finite element approximation of the maxwell problem suitable for singular solutions a new mixed finite element approximation of maxwell s problem is proposed its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term which yields a very weak control on the divergence of the unknown the method is shown to be stable and convergent in the natural h rm mathbf curl 0 omega norm for this unknown in particular convergence also applies to singular solutions for which classical nodal based interpolations are known to suffer from spurious convergence upon mesh refinement

analysis of a continuous finite element method for h mathrm curl mathrm div elliptic interface problem in this paper we develop a continuous finite element method for the curlcurl grad div vector second order elliptic problem in a three dimensional polyhedral domain occupied by discontinuous nonhomogeneous anisotropic materials in spite of the fact that the curlcurl grad div interface problem is closely related to the elliptic interface problem of vector laplace operator type the continuous finite element discretization of the standard variational problem of the former generally fails to give a correct solution even in the case of homogeneous media whenever the physical domain has reentrant corners and edges to discretize the curlcurl grad div interface problem by the continuous finite element method we apply an element local l 2 projector to the curl operator and a pseudo local l 2 projector to the div operator where the continuous lagrange linear element enriched by suitable element and face bubbles may be employed it is shown that the finite element problem retains the same coercivity property as the continuous problem an error estimate mathcal o h r in an energy norm is obtained between the analytical solution and the continuous finite element solution where the analytical solution is in prod l 1 l h r omega l 3 for some r in 1 2 1 due to the domain boundary reentrant corners and edges e g nonconvex polyhedron and due to the interfaces between the different material domains in omega bigcup l 1 l omega l

fractional derivative estimates in gevrey spaces global regularity and decay for solutions to semilinear equations in rn abstract we propose a unified functional analytic approach to study the uniform analytic gevrey regularity and the decay of solutions to semilinear elliptic equations on r n first we develop a fractional calculus for nonlinear maps in banach spaces of l p based gevrey functions 1 h p s r n regularity with s scr 0 depending on the nonlinearity next we investigate the type of decay polynomial or exponential of the derivatives of solutions to semilinear elliptic equations provided they decay a priori slowly as o x x for some small 0 the restrictions involved in our results are optimal in particular given a hyperplane l we construct 2d 2 strongly singular solutions locally in h p s r n for s

long time stability of high order multistep numerical schemes for two dimensional incompressible navier stokes equations the long time stability properties of a few multistep numerical schemes for the two dimensional incompressible navier stokes equations formulated in vorticity stream function are investigated in this article these semi implicit numerical schemes use a combination of explicit adams bashforth extrapolation for the nonlinear convection term and implicit adams moulton interpolation for the viscous diffusion term up to fourth order accuracy in time as a result only two poisson solvers are needed at each time step to achieve the desired temporal accuracy the fully discrete schemes with fourier pseudospectral approximation in space are analyzed in detail with the help of a priori analysis and aliasing error control techniques we prove uniform in time bounds for these high order schemes in both l 2 and h m norms for m ge 1 provided that the time step is bounded by a given constant such a long time stability is also demonstrated by the numerical experiments

well posedness and regularity of the generalized burgers equation in periodic gevrey spaces we consider the generalized burgers equation in a class of gevrey functions g s t we show that the generalized burgers equation is well posed in this space furthermore we show that the solution is gevrey in the spacial variable and gevrey 2 in the time variable

bifurcation of critical points for solutions of the 2d euler and 2d quasi geostrophic equations we consider the 2d euler and 2d quasi geostrophic equations with periodic boundary conditions for both systems we will use the stream function formulation and study the bifurcation problem for the critical points of the stream function in a small neighborhood of the origin we construct a set of initial data such that initial critical points of the stream function bifurcate from 1 to 2 and then to 3 critical points in finite time for the quasi geostrophic equation the whole bifurcation process takes place strictly within the lifespan of the constructed local solution

a combined nodal continuous discontinuous finite element formulation for the maxwell problem abstract continuous galerkin formulations are appealing due to their low computational cost whereas discontinuous galerkin formulation facilitate adaptative mesh refinement and are more accurate in regions with jumps of physical parameters since many electromagnetic problems involve materials with different physical properties this last point is very important for this reason in this article we have developed a combined cg dg formulation for maxwell s problem that allows arbitrary finite element spaces with functions continuous in patches of finite elements and discontinuous on the interfaces of these patches in particular the second formulation we propose comes from a novel continuous galerkin formulation that reduces the amount of stabilization introduced in the numerical system in all cases we have performed stability and convergence analyses of the methods the outcome of this work is a new approach that keeps the low cpu cost of recent nodal continuous formulations with the ability to deal with coefficient jumps and adaptivity of discontinuous ones all these methods have been tested using a problem with singular solution and another one with different materials in order to prove that in fact the resulting formulations can properly deal with these problems

existence and generalized gevrey regularity of solutions to the kuramoto sivashinsky equation in rn abstract motivated by the work of foias and temam c foias r temam gevrey class regularity for the solutions of the navier stokes equations j funct anal 87 1989 359 369 we prove the existence and gevrey regularity of local solutions to the kuramoto sivashinsky equation in r n with initial data in the space of distributions the control on the gevrey norm provides an explicit estimate of the analyticity radius in terms of the initial data in the particular case when n 1 our analysis allows for initial data that are less smooth than that considered by grujic and kukavica z grujic i kukavica space analyticity for the navier stokes and related equations with initial data in l p j funct anal 152 1998 447 466

the approximation of the maxwell eigenvalue problem using a least squares method in this paper we consider an approximation to the maxwell s eigenvalue problem based on a very weak formulation of two div curl systems with complementary boundary conditions we formulate each of these div curl systems as a general variational problem with different test and trial spaces i e the solution space is l 2 l 2 3 and components in the test spaces are in subspaces of h 1 the sobolev space of order one on the computational domain q a finite element least squares approximation to these variational problems is used as a basis for the approximation using the structure of the continuous eigenvalue problem a discrete approximation to the eigenvalues is set up involving only the approximation to either of the div curl systems we give some theorems that guarantee the convergence of the eigenvalues to those of the continuous problem without the occurrence of spurious values finally some results of numerical experiments are given

computation of maxwell singular solution by nodal continuous elements abstract in this paper we propose and analyze a nodal continuous and h 1 conforming finite element method for the numerical computation of maxwell s equations with singular solution in a fractional order sobolev space h r where r may take any value in the most interesting interval 0 1 the key feature of the method is that mass lumping linear finite element l 2 projections act on the curl and divergence partial differential operators so that the singular solution can be sought in a setting of l 2 space we shall use the nodal continuous linear finite elements enriched with one element bubble in each element to approximate the singular and non h 1 solution discontinuous and nonhomogeneous media are allowed in the method some error estimates are given and a number of numerical experiments for source problems as well as eigenvalue problems are presented to illustrate the superior performance of the proposed method

the algebraic approximation of attractors the finite dimensional case abstract in this article we present a constructive method for approximating attractors the approximate sets are parts of algebraic sets i e the zeros of high degree polynomial functions and they can approximate the attractor at an arbitrary high level of accuracy

decoupled schemes for unsteady mhd equations ii finite element spatial discretization and numerical implementation in this article a decoupled fully discrete scheme for solving 2d magnetohydrodynamics mhd equations is proposed the decoupled scheme is used for time discretization and the finite element method is used for spatial discretization firstly the almost unconditional stability t c of this scheme is established then optimal l2 and h1 error estimates of numerical solution are provided finally a numerical example is presented to confirm our theoretical results and show the high efficiency of the decoupled scheme

invariant subspaces of the periodic navier stokes and magnetohydrodynamics equations symmetries and inverse cascades it is shown that when the initial condition and the forcing term of the periodic navier stokes or magnetohydrodynamics equations have fourier coefficients which vanish outside a certain semigroup of frequencies the same happens to the solutions for all time subgroups of frequencies correspond to solutions possessing certain symmetries by taking as a semigroup the frequencies whose fourier components are non negative integers we get a class of solutions for which the higher modes do not influence the evolution of the lower ones therefore the phenomenon of inverse cascading cannot occur for them

computational scales of sobolev norms with application to preconditioning this paper provides a framework for developing computationally efficient multilevel preconditioners and representations for sobolev norms specifically given a hilbert space v and a nested sequence of subspaces v 1 c v 2 c c v we construct operators which are spectrally equivalent to those of the form a k k q k q k 1 here k k 1 2 are positive numbers and q k is the orthogonal projector onto v k with q 0 0 we first present abstract results which show when a is spectrally equivalent to a similarly constructed operator a defined in terms of an approximation q k of q k for k 1 2 we show that these results lead to efficient preconditioners for discretizations of differential and pscudo differential operators of positive and negative order these results extend to sums of operators for example singularly perturbed problems such as i e can be preconditioned uniformly independently of the parameter e we also show how to precondition an operator which results from tikhonov regularization of a problem with noisy data finally we describe how the technique provides computationally efficient bounded discrete extensions which have applications to domain decomposition

on depletion of the vortex stretching term in the 3d navier stokes equations certain new cancellation properties in the vortex stretching term are detected leading to new geometric criteria for preventing finite time blow up in the 3d navier stokes equations

a nonconforming finite element method for a two dimensional curl curl and grad div problem a numerical method for a two dimensional curl curl and grad div problem is studied in this paper it is based on a discretization using weakly continuous p 1 vector fields and includes two consistency terms involving the jumps of the vector fields across element boundaries optimal convergence rates up to an arbitrary positive epsilon in both the energy norm and the l 2 norm are established on graded meshes the theoretical results are confirmed by numerical experiments

a unified analysis for coded ds cdma with equal gain chip combining in the downlink of ofdm systems this paper presents a novel unified analysis for the bit error rate in the downlink of convolutionally coded and single user detected multicarrier code division multiple access cdma multicarrier direct sequence cdma time and frequency domain spreading cdma and orthogonal frequency division multiple access performance is analyzed under the assumption of hadamard spreading codes equal gain chip combining and a highly correlated frequency selective rayleigh fading channel closed form expressions are presented for the cumulative distribution function probability distribution function and moment generating function for the signal to noise plus interference ratio after despreading the presented results assume error free channel estimates a perfectly synchronized receiver and are found to reasonably well agree with simulation results

orthogonal multiple access over time and frequency selective channels suppression of multiuser interference mui and mitigation of time and frequency selective doubly selective channel effects constitute major challenges in the design of third generation wireless mobile systems relying on a basis expansion model bem for doubly selective channels we develop a channel independent block spreading scheme that preserves mutual orthogonality among single cell users at the receiver this alleviates the need for complex multiuser detection and enables separation of the desired user by a simple code matched channel independent block despreading scheme that is maximum likelihood ml optimal under the bem plus white gaussian noise assumption on the channel in addition each user achieves the maximum delay doppler diversity for gaussian distributed bem coefficients issues like links with existing multiuser transceivers existence user efficiency special cases backward compatibility with direct sequence code division multiple access ds cdma and error control coding are briefly discussed

on approximate inertial manifolds for two and three dimensional turbulent flows abstract in this paper we present some results concerning finite dimensional analytic manifolds that approximate the global attractor and the structure of the small eddies for the navier stokes equations under periodic boundary conditions we show that the smoother the external force the better the approximation

weighted regularization of maxwell equations in polyhedral domains we present a new method of regularizing time harmonic maxwell equations by a bf grad div term adapted to the geometry of the domain this method applies to polygonal domains in two dimensions as well as to polyhedral domains in three dimensions in the presence of reentrant corners or edges the usual regularization is known to produce wrong solutions due the non density of smooth fields in the variational space we get rid of this undesirable effect by the introduction of special weights inside the divergence integral standard finite elements can then be used for the approximation of the solution this method proves to be numerically efficient

on an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics in this work we propose a new stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations the novelty of this formulation is the fact that it always converges to the physical solution even for singular ones a detailed set of numerical experiments have been performed in order to validate our approach

ill posedness for the navier stokes equations in critical besov spaces b q 1 abstract we study the cauchy problem for the incompressible navier stokes equations in two and higher spatial dimensions 0 1 u t u u u p 0 div u 0 u 0 x u 0 for arbitrarily small 0 we show that the solution map u 0 u in critical besov spaces b q 1 q 1 2 is discontinuous at origin it is known that the navier stokes equation is globally well posed for small data in bmo 1 20 taking notice of the embedding b q 1 bmo 1 q 2 we see that for sufficiently small 0 u 0 b q 1 q 2 can guarantee that 0 1 has a unique global solution in bmo 1 however this solution is instable in b q 1 and the solution can have an inflation in b q 1 for certain initial data

a mixed finite element method with exactly divergence free velocities for incompressible magnetohydrodynamics abstract we introduce and analyze a mixed finite element method for the numerical discretization of a stationary incompressible magnetohydrodynamics problem in two and three dimensions the velocity field is discretized using divergence conforming brezzi douglas marini bdm elements and the magnetic field is approximated by curl conforming nedelec elements the h 1 continuity of the velocity field is enforced by a dg approach a central feature of the method is that it produces exactly divergence free velocity approximations and captures the strongest magnetic singularities we prove that the energy norm error is convergent in the mesh size in general lipschitz polyhedra under minimal regularity assumptions and derive nearly optimal a priori error estimates for the two dimensional case we present a comprehensive set of numerical experiments which indicate optimal convergence of the proposed method for two dimensional as well as three dimensional problems

kraichnan turbulence via finite time averages relations central to kraichnan s theory of fully developed two dimensional turbulence are rigorously established for finite time averages in particular we prove that if the ratio of the averages of palinstrophy to enstrophy is large then a large inertial range displaying an enstrophy cascade exists moreover if this ratio is comparable up to a logarithm to the dissipation wave number a necessary condition for turbulence then the power law for the energy spectrum until now derived only heuristically is rigorously shown to provide up to a logarithm an upper bound for the energy spectrum finally we show that deep in the dissipation range the palinstrophy contributed by eddies smaller than a specified length decays exponentially in the corresponding wave number the averaging times needed for these relations are bounded in terms of the generalized grashof number independent of the solution for which the time averages are taken solutions are not assumed to be on the global attractor merely within the absorbing ball an easily verified condition

computing electromagnetic eigenmodes with continuous galerkin approximations costabel and dauge proposed a variational setting to solve numerically the time harmonic maxwell equations in 3d polyhedral geometries with a continuous approximation of the electromagnetic field in order to remove spurious eigenmodes three computational strategies are then possible the original method which requires a parameterization of the variational formulation the second method which is based on an a posteriori filtering of the computed eigenmodes and the third method which uses a mixed variational setting so that all spurious modes are removed a priori in this paper we discuss the relative merits of the approaches which are illustrated by a series of 3d numerical examples 2008 elsevier b v all rights reserved

nodal based finite element methods with local projection stabilization for linearized incompressible magnetohydrodynamics abstract we consider the linearized resistive magnetohydrodynamics mhd model in incompressible media and its numerical solution conforming nodal based finite element approximations of the mhd model both for inf sup stable and equal order finite elements with respect to velocity and pressure are considered as opposed to a residual based stabilization method by badia et al 2013 we consider a local projection stabilization for the numerical solution a detailed stability and error analysis for the arising discrete problem is given some numerical experiments like hartmann s mhd problem and singular solutions are examined

gevrey regularity of mild solutions to the parabolic elliptic system of drift diffusion type in critical besov spaces abstract this paper is devoted to studying analyticity of mild solutions to the parabolic elliptic system of drift diffusion type with small initial data in critical besov spaces more precisely by using multilinear singular integrals and fourier localization argument we show that global in time mild solutions are gevrey regular i e e t 1 v e t 1 w l t b p r 2 n p r n l t 1 b p r n p r n for all 1 p 2 n and 1 r where 1 is the fourier multiplier whose symbol is given by 1 i 1 n i as a corollary we obtain decay estimates of mild solutions in critical besov spaces without using cumbersome recursive estimation of higher order derivatives

a new approximation technique for div curl systems in this paper we describe an approximation technique for div curl systems based in l where is a domain in 3 we formulate this problem as a general variational problem with different test and trial spaces the analysis requires the verification of an appropriate inf sup condition this results is a very weak formulation where the solution space is l and the data reside in various negative norm spaces subsequently we consider finite element approximations based on this weak formulation the main approach of this paper involves the development of stable pairs of discrete test and trial spaces with this approach we enlarge the test space so that the discrete inf sup condition holds and use a negative norm least squares formulation to reduce to a uniquely solvable linear system this leads to optimal order estimates for problems with minimal regularity which is important since it is possible to construct magnetostatic field problems whose solutions have low sobolev regularity e g h with 0 s 1 2 the resulting algebraic equations are symmetric positive definite and well conditioned a second approach using a smaller test space which adds terms to the form for stabilization will also be mentioned some numerical results are also presented

the dissipative scale of the stochastics navier stokes equation regularization and analyticity we prove spatial analyticity for solutions of the stochastically forced navier stokes equation provided that the forcing is sufficiently smooth spatially we also give estimates which extend to the stationary regime providing strong control of both of the expected rate of dissipation and fluctuations about this mean surprisingly we could not obtain non random estimates of the exponential decay rate of the spatial fourier spectra

on the hydrostatic approximation of the navier stokes equations in a thin strip abstract in this paper we first prove the global well posedness of a scaled anisotropic navier stokes system and the hydrostatic navier stokes system in a 2 d striped domain with small analytic data in the tangential variable then we justify the limit from the anisotropic navier stokes system to the hydrostatic navier stokes system with analytic data