pressure schur complement preconditioners for the discrete oseen problem we consider several preconditioners for the pressure schur complement of the discrete steady oseen problem two of the preconditioners are well known from the literature and the other is new supplemented with an appropriate approximate solve for an auxiliary velocity subproblem these approaches give rise to a family of the block preconditioners for the matrix of the discrete oseen system in the paper we critically review possible advantages and difficulties of using various schur complement preconditioners we recall existing eigenvalue bounds for the preconditioned schur complement and prove such for the newly proposed preconditioner these bounds hold both for lbb stable and stabilized finite elements results of numerical experiments for several model two dimensional and three dimensional problems are presented in the experiments we use lbb stable finite element methods on uniform triangular and tetrahedral meshes one particular conclusion is that in spite of essential improvement in comparison with simple scaled mass matrix preconditioners in certain cases none of the considered approaches provides satisfactory convergence rates in the case of small viscosity coefficients and a sufficiently complex e g circulating advection vector field

torsion freeness of symmetric powers of ideals let i be an ideal in a noetherian commutative ring r with unit let k 2 be an integer and let k i s k i i k be the canonical surjective r module homomorphism from the kth symmetric power of i to the kth power of i when pd r i 1 or when i is a perfect gorenstein ideal of grade 3 we provide a necessary and sufficient condition for k to be an isomorphism in terms of upper bounds for the minimal number of generators of the localisations of i when i m is a maximal ideal of r we show that is an isomorphism if and only if r m is a regular local ring in all three cases for i our results yield that if is an isomorphism then at is also an isomorphism for each 1 t k

an adaptive finite element method for the h ψ formulation of time dependent eddy current problems in this paper we develop an adaptive finite element method based on reliable and efficient a posteriori error estimates for the h formulation of eddy current problems with multiply connected conductors multiply connected domains are considered by making cuts the competitive performance of the method is demonstrated by an engineering benchmark problem team workshop problem 7 and a singular problem with analytic solution

sequences of linear type let a be a commutative ring 91 an ideal of a s 2l the symmetric algebra of 8 and r vl the recs algebra of vi there is a canonical surjection x s k which is homogeneous of degree zro and therefore gives canonical surjcctions r f 91 for every integer t 3 0 many recent papers 1 2 4 5 7 cc have investigated the problem of determining which ideals 91 have the property that a is an isomorphism such ideals have been dubbed ideals of lineur type s for example huneke showed that every ideal generated by a d sequence is of linear type 71 if ii is generated by n elements a a then for t 3 i there is an exact scquencc

the solvability of coupling the thermal effect and magnetohydrodynamics field with turbulent convection zone and the flow field abstract in this paper the magneto heating coupling model is studied in details with turbulent convection zone and the flow field involved our main work is to analyze the well posed property of this model with the regularity techniques we present the weak formulation of the coupled magneto heating model and establish the regularity problem using rothe s method monotone theories of nonlinear operator weak convergence theories we prove that the limits of the solutions from rothe s method converge to the solutions of the regularity problem with proper initial data with the help of the spacial regularity technique we derive the well posedness of the original problems when the regular parameter 0 moreover with additional regularity assumption for both the magnetic field and temperature variable we prove the uniqueness of the solutions

an h ψ formulation for the three dimensional eddy current problem in laminated structures it is a very challenging problem for the direct simulation of the three dimensional eddy currents in grain oriented go silicon steel laminations since the coating fllm is only several microns thick over each lamination and the magnetic permeability is nonlinear and anisotropic in addition the system of go silicon steel laminations has multiple scales and the ratio of the largest scale to the smallest scale can be up to 10 6 in this paper we study an h formulation for the nonlinear eddy current problem in laminated conductors by omitting the insulating fllms between neighboring laminations we propose an approximate but efiective h formulation for the nonlinear eddy current problem which reduces the scale ratio by 2 3 orders of magnitude the well posedness of the original problem and the approximate problem are established by examining their weak formulations the convergence is proved for the solution of the approximate problem to the solution of the original problem as the thickness of coating fllms approaches zero

on the injectivity of blowing up ring morphisms abstract let i x 1 x r be a finitely generated ideal in a commutative ring r and let n 2 be an integer let i n s n i i n be the canonical morphism from the nth symmetric power of i onto the nth power of i recently tchernev asked for when i n being an isomorphism implies that i p is an isomorphism for each 2 p n we give an affirmative answer provided that the ideal j x 1 x r 1 verifies that j p s p j j p is an isomorphism for all 2 p n in addition for every n 2 we give an example of an ideal i such that i p is an isomorphism for all p n 1 and i n is not

hilbert function of powers of ideals of low codimension we study the hilbert function of the powers of homogeneous ideals which are either cohen macaulay of codimension 2 or gorenstein of codimension 3 we show that that if i is an ideal in one of these classes and it is of linear type then for all k the hilbert function of i k depends only on the hilbert function of i in other words if i andj are ideals in one of the above mentioned classes which are both of linear type and they have the same hilbert function then also i k and j k have the same hilbert function for all k

factorization methods for the numerical approximation of navier stokes equations we investigate a general approach for the numerical approximation of incompressible navier stokes equations based on splitting the original problem into successive subproblems which are cheaper to solve the splitting is obtained through an algebraic approximate factorization of the matrix arising from space and time discretization of the original equations several schemes based on approximate factorization are investigated for some of these methods a formal analogy with well known time advancing schemes such as the projection chorin temam s can be pointed out features and limits of this analogy that was earlier introduced in b perot j comp phys 108 1993 51 8 are addressed other new methods can also be formulated starting from this approach in particular we introduce the so called yosida method which can be investigated in the framework of quasi compressibility schemes numerical results illustrating the different performances of the different methods addressed are presented for a couple of test cases

intersection theory of linear embeddings we study intersection theoretic properties of subschemes defined by ideal sheaves of linear type in particular their behavior with respect to blowups and segre classes

superconvergence analysis of two grid fem for maxwell s equations with a thermal effect abstract based on two grid algorithm we develop the superconvergence analysis of fully discrete scheme with the lowest order nedelec element and crank nicolson scheme for the magneto heat coupling model which is also considered as maxwell s equations with a thermal effect then main process of numerical analysis has two parts on one hand we utilize newton type taylor expansion on superconvergent solutions for those nonlinear terms on coarse mesh differing from the numerical solution which makes our given two grid method successful on the other hand we prove the solutions on the fine mesh to be higher accuracy by the postprocessing interpolation technique such a design is conducive to improving the computational accuracy in space and decreasing time consumption simultaneously by employing the skill we can obtain the convergent rate of o t 2 h 2 h 3 which means that the space mesh size should satisfy h o h 3 2 finally the numerical example is presented to verify the theoretical results

an analysis of the fractional step method the fractional step method for solving the incompressible navier stokes equations in primitive variables is analyzed as a block lu decomposition in this formulation the issues involving boundary conditions for the intermediate velocity variables and the pressure are clearly resolved in addition it is shown that poor temporal accuracy first order is not due to boundary conditions but due to the method itself a generalized block lu decomposition that overcomes this difficulty is presented allowing arbitrarily high temporal order of accuracy the generalized decomposition is shown to be useful for a wide range of problems including steady problems technical issues such as stability and the appropriate pressure update scheme are also addressed numerical simulations of the steady incompressible navier stokes equations in a square domain confirm the theoretical results 18 refs 4 figs

a delta regularization finite element method for a double curl problem with divergence free constraint to deal with the divergence free constraint in a double curl problem rm curl mu 1 rm curl u f and rm div varepsilon u 0 in omega where mu and varepsilon represent the physical properties of the materials occupying omega we develop a delta regularization method rm curl mu 1 rm curl u delta delta varepsilon u delta f to completely ignore the divergence free constraint rm div varepsilon u 0 we show that u delta converges to u in h rm curl omega norm as delta rightarrow 0 the edge finite element method is then analyzed for solving u delta with the finite element solution u delta h a quasioptimal error bound in the h rm curl omega norm is obtained between u and u delta h including a uniform with respect to delta stability of u delta h in the h rm curl omega norm all the theoretical analysis is done in a general setting where mu and varepsilon may be discontinuous an

two grid method for compressible miscible displacement problem by cfem mfem abstract this paper is concerned about the error analysis of two grid method for compressible miscible displacement in porous medium a characteristics finite element method cfem is presented for the concentration equation to handle the convection part and standard mixed finite element method mfem is used for the pressure equation moreover we linearize the equations based on the newton iteration method then two grid method is considered in this full discrete scheme problem we prove the l p error estimates for the pressure darcy velocity concentration variables in the two grid method it is shown that coarse space can be extremely coarse and we achieve asymptotically optimal approximation finally numerical experiment indicates that two grid method is a very effective method for solving miscible displacement problem

homogenization of the problem of eddy currents in a transformer core an electric transformer core constituted of two thin sheets is considered one sheet is metallic and the other is insulator which is a dielectric these two sheets are rolled up in the form of a cylinder a periodic difference of potential is applied between the two ends of the metallic sheets the purpose of this paper is to use a homogenization technique to describe the eddy currents that are developing in the transformer core the limit problem corresponds to a modified ohm s law with an average conductivity and a zero radial component of the current

on discrete projection methods for the incompressible navier stokes equations an algorithmical approach abstract we derive a general class of iteration schemes for the incompressible navier stokes equations which contains fully coupled solution techniques as well as operator splitting projection methods we combine the advantages of both namely accuracy stability and efficiency and obtain a special form of discrete projection schemes in combination with a nonlinear iteration of quasi newton type one may use these schemes analogously to the well known pure projection schemes e g of chorin and van kan or apply them as preconditioners in a defect correction approach to obtain the fully coupled galerkin solution the corresponding complexity analysis shows that in combination with certain nonconforming finite element discretizations a huge gain in efficiency may be obtained particularly in the highly nonstationary case our theoretical results are confirmed by comparative numerical tests for both types of schemes it turns out that the appropriate time steps for the pure projection approach are only moderately smaller than those for the fully implicitly coupled schemes but that the work to obtain comparative results with the discrete projection methods as solvers is much lower an interesting observation is that in the case of higher reynolds numbers no significant pressure boundary layers occur even for the pure projection schemes these considerations and first numerical tests in 3d give hope to obtain a powerful cfd tool

a novel two grid method for semilinear elliptic equations a new finite element discretization technique based on two coarse and fine subspaces is presented for a semilinear elliptic boundary value problem the solution of a nonlinear system on the fine space is reduced to the solution of two small one linear and one nonlinear systems on the coarse space and a linear system on the fine space it is shown both theoretically and numerically that the coarse space can be extremely coarse and still achieve asymptotically optimal approximation as a result the numerical solution of such a nonlinear equation is not significantly more expensive than the solution of one single linearized equation

long time behavior of the two grid finite element method for fully discrete semilinear evolution equations with positive memory abstract based on two grid discretizations two fully discrete finite element algorithms for semilinear parabolic integro differential equations with positive memory are proposed with the backward euler scheme for the temporal discretization the basic idea of the space two grid finite element algorithms is to approximate the semilinear equations on a coarse space grid and to solve the linearized equations on a finer space grid at each time step to further decreases the amount of computational work a space time two grid algorithm based on a coarse space grid with large time stepsize t and a finer space grid with small time stepsize t for the evolutional equations is proposed in this paper the sharp long time stability and error estimates for the standard finite element method the space two grid finite element method and the space time two grid finite element method are derived it is showed that the two grid algorithms long time stability and error estimates are similar to those of the direct resolution of the semilinear problem on a fine grid

an adaptive multilevel method for time harmonic maxwell equations with singularities we develop an adaptive edge finite element method based on reliable and efficient residual based a posteriori error estimates for low frequency time harmonic maxwell equations with singularities the resulting discrete problem is solved by the multigrid preconditioned minres minimum residual iteration algorithm we demonstrate the efficiency and robustness of the proposed method by extensive numerical experiments for cavity problems with singular solutions which include in particular scattering over screens

a discrete projection method for incompressible viscous flow with coriolis force the paper presents a new discrete projection method for the numerical solution of the navier stokes equations with coriolis force term on an algebraic level we interpret one time step of the projection method as an incomplete factorization of the linearized navier stokes system and as the iteration of an uzawa type algorithm with special preconditioning for the pressure block this enables us to modify the well known projection method in a way to account for possibly dominating coriolis terms we consider a special multigrid method for solving the velocity subproblems and a modified projection pressure correction step results of numerical tests are presented for a model problem as well as for 3d flow simulations in stirred tank reactors

navier stokes equations in rotation form a robust multigrid solver for the velocity problem the topic of this paper is motivated by the navier stokes equations in rotation form linearization and application of an implicit time stepping scheme results in a linear stationary problem of oseen type in well known solution techniques for this problem such as the uzawa or schur complement method a subproblem consisting of a coupled nonsymmetric system of linear equations of diffusion reaction type must be solved to update the velocity vector field in this paper we analyze a standard finite element method for the discretization of this coupled system and we introduce and analyze a multigrid solver for the discrete problem both for the discretization method and the multigrid solver the question of robustness with respect to the amount of diffusion and variation in the convection field is addressed we prove stability results and discretization error bounds for the galerkin finite element method we present a convergence analysis of the multigrid method which shows the robustness of the solver results of numerical experiments are presented which illustrate the stability of the discretization method and the robustness of the multigrid solver

block implicit multigrid solution of navier stokes equations in primitive variables abstract a calculation procedure for rapid computation of steady multidimensional viscous flows is presented the method solves the navier stokes equations in primitive variables using a coupled block implicit multigrid procedure the procedure is applicable to finite difference formulations using staggered locations of the flow variables a smoothing technique called symmetrical coupled gauss seidel scgs is proposed and is empirically observed to provide good smoothing rates the viscous flow in a square cavity with a moving top wall is calculated for a range of reynolds numbers calculations with finite difference grids as large as 321 321 nodes have been made to test the accuracy and efficiency of the calculation scheme the cpu times for these calculations are observed to be significantly smaller than other solution algorithms with primitive variable formulation the calculated flow fields in the cavity are in good agreement with earlier studies of the same flow situation