adaptive poromechanics computations based on a posteriori error estimates for fully mixed formulations of biot s consolidation model abstract this paper is concerned with the analysis of coupled mixed finite element methods applied to the biot s consolidation model we consider two mixed formulations that use the stress tensor and darcy velocity as primary variables as well as the displacement and pressure the first formulation is with a symmetric stress tensor while the other enforces the symmetry of the stress weakly through the introduction of a lagrange multiplier the well posedness of the two formulations is shown through galerkin s method and suitable a priori estimates the two formulations are then discretized with the backward euler scheme in time and with two mixed finite elements in space we present next a general and unified a posteriori error analysis which is applicable for any flux and stress conforming discretization our estimates are based on h 1 conforming reconstruction of the pressure and a suitable h 1 d conforming reconstruction of the displacement both are continuous and piecewise affine in time these reconstructions are used to infer a guaranteed and fully computable upper bound on the energy type error measuring the differences between the exact and the approximate pressure and displacement the error components resulting from the spatial and the temporal discretization are distinguished they are then used to design an adaptive space time algorithm numerical experiments illustrate the efficiency of our estimates and the performance of the adaptive algorithm

galerkin finite element methods with symmetric pressure stabilization for the transient stokes equations stability and convergence analysis we consider the stability and convergence analysis of pressure stabilized finite element approximations of the transient stokes equation the analysis is valid for a class of symmetric pressure stabilization operators but also for standard inf sup stable velocity pressure spaces without stabilization provided the initial data are chosen as a specific method dependent ritz projection we get unconditional stability and optimal convergence for both pressure and velocity approximations in natural norms for arbitrary interpolations of the initial data a condition between the space and time discretization parameters has to be verified in order to guarantee pressure stability

language equations with complementation expressive power consider a system of language equations of the form xi i x1 xn 1 i n where every i may contain the operations of concatenation and complementation these systems have been studied in language equations with complementation decision problems a okhotin o yakimova theoretical computer science 376 2007 112 126 this paper investigates the family of languages representable by unique solutions of such systems a method for proving nonrepresentability of particular languages is developed several natural subfamilies of this family are compared to each other and to the main known families of formal languages their position in the hierarchy is established

finite element approximation of the nonstationary navier stokes problem part ii stability of solutions and error estimates uniform in time in this paper assumptions about the stability of a solution are introduced in the numerical analysis of the nonstationary navier stokes problem for the purpose of extending local a priori error estimates and local a posteriori error estimates globally in time

on a multiscale approach to the transient stokes problem dynamic subscales and anisotropic space time discretization abstract in this article we analyze some residual based stabilization techniques for the transient stokes problem when considering anisotropic time space discretizations we define an anisotropic time space discretization as a family of time space partitions that does not satisfy the condition h 2 c t with c uniform with respect to h and t standard residual based stabilization techniques are motivated by a multiscale approach approximating the effect of the subscales onto the large scales one of the approximations is to consider the subscales quasi static neglecting their time derivative it is well known that these techniques are unstable for anisotropic time space discretizations we show that the use of dynamic subscales where the subscales time derivatives are not neglected solves the problem and prove optimal convergence and stability results that are valid for anisotropic time space discretizations also the improvements related to the use of orthogonal subscales are addressed

on constraint preservation in numerical simulations of yang mills equations the problem of constraint preservation for discretizations of nonlinear pdes is addressed in the example of the hyperbolic yang mills equations in temporal gauge these equations preserve a nonlinear divergence field analogous to the electric charge for maxwell s equations we introduce and discuss several discretizations of these equations on finite element spaces of lie algebra valued differential forms numerical experiments indicate that simply restricting the variational formulation to the galerkin spaces yields substantial drift in the charge contrary to the linear maxwell case we then propose a fully discrete method constrained with lagrange multipliers for which we prove discrete charge conservation and observe excellent energy conservation

non linear vibrations of a beam resting on a tensionless winkler foundation the forced vibrations of an elastic beam resting on a non linear tensionless winkler foundation subjected to a concentrated dynamic load at its centre are described in this paper the problem is a non linear one because of the tensionless character of the foundation and the non linear term in the foundation model a non linear governing differential equation for the forced vibrations of the beam is derived in matrix form by employing the galerkin method the free vibration mode functions of the completely free beam are adopted as the co ordinate functions of the displacement function of the beam firstly the static solution is obtained and the contact length is determined this is then used as an initial configuration of the forced vibrations the results which represent the static and dynamic responses of the beam for linear and non linear cases are presented in the figures

three dimensional finite element methods for the stokes problem the tetrahedral finite element approximation of the stokes problem is analyzed by means of polynomials piecewise of degree k 1 for the velocity and continuous piecewise of degree k for the pressure a stability result is given for every k ge 1

eigenvalue approximation by mixed and hybrid methods note univ maryland dept math college pk md 20742 ecole polytech ctr math appl f 91128 palaiseau france univ paris 6 f 75230 paris 05 france mercier b cea limeil f 94190 villeneuve france isi document delivery no lq584times cited 29cited reference count 44 reference asn article 1981 005doi 10 2307 2007651 record created on 2006 08 24 modified on 2017 05 12

complexity classes without machines on complete languages for up this paper develops techniques for studying complexity classes that are not covered by known recursive enumerations of machines often counting classes probabilistic classes and intersection classes lack such enumerations concentrating on the counting class up we show that there are relativizations for which upa has no complete languages and other relativizations for which pb upb npb and upb has complete languages among other results we show that p up if and only if there exists a set s in p of boolean formulas with at most one satisfying assignment such that s sat is not in p p up coup if and only if there exists a set s in p of uniquely satisfiable boolean formulas such that no polynomial time machine can compute the solutions for the formulas in s if up has complete languages then there exists a set r in p of boolean formulas with at most one satisfying assignment so that sat r is complete for up finally we indicate the wide applicability of our techniques to counting and probabilistic classes by using them to examine the probabilistic class bpp there is a relativized world where bppa has no complete languages if bpp has complete languages then it has a complete language of the form b majority where b p and majority f f is true for at least half of all assignments is the canonical pp complete set

analytical solutions for steady state responses of an infinite euler bernoulli beam on a nonlinear viscoelastic foundation subjected to a harmonic moving load abstract the paper deals with the steady state responses of an infinite euler bernoulli beam resting on a nonlinear foundation under a harmonic moving load greatly different from previous works the nonlinear partial differential governing equation of the beam motion is converted to two nonlinear volterra integral equations by using the fourier transform residues theorem and the convolution theorem the volterra integral equations have four different expressions depending on the damping coefficient of the foundation the linear part of the foundation stiffness and the frequency of the moving load the modified adomian decomposition method in conjunction with a simple iterative formula derived from the integral equation theorems are applied to obtain analytical solutions for the steady state responses of the beam the closed form solutions presented in this paper do not contain complicated infinite integrals which are better to show the influence of the nonlinear part of foundation stiffness the parametric study shows that the nonlinear part of foundation stiffness affects not only qualitative but also quantitative analysis results of the infinite euler bernoulli beam under a harmonic moving load

computing functions with parallel queries to np the class 2p of languages polynomial time truth table reducible to sets in np has a wide range of different characterizations we consider several functional versions of 2p based on these characterizations we show that in this way the three function classes fllognp fplognp and fp np are obtained in contrast to the language case the function classes seem to all be different we give evidence in support of this fact by showing that fllognp coincides with any of the other classes then l p and that the equality of the classes fplognp and fp np would imply that the number of nondeterministic bits needed for the computation of any problem in np can be reduced by a polylogarithmic factor and that the problem can be computed deterministically with a subexponential time bound of order 2no 1 log log n

analysis of finite element approximation of evolution problems in mixed form this paper deals with the finite element approximation of evolution problems in mixed form following d boffi f brezzi and l gastaldi math comp 69 2000 pp 121 140 we handle separately two types of problems a model for the first case is the heat equation in mixed form while the time dependent stokes problem fits within the second one for either case we give sufficient conditions for a good approximation in the natural functional spaces the results are not obvious in the first situation in this case the well known conditions for the well posedness and convergence of the corresponding steady problem are not sufficient for the good approximation of the time dependent problem this issue is demonstrated with a numerical counter example and justified analytically

quadrilateral h div finite elements we consider the approximation properties of quadrilateral finite element spaces of vector fields defined by the piola transform extending results previously obtained for scalar approximation the finite element spaces are constructed starting with a given finite dimensional space of vector fields on a square reference element which is then transformed to a space of vector fields on each convex quadrilateral element via the piola transform associated to a bilinear isomorphism of the square onto the element for affine isomorphisms a necessary and sufficient condition for approximation of order r 1 in l2 is that each component of the given space of functions on the reference element contain all polynomial functions of total degree at most r in the case of bilinear isomorphisms the situation is more complicated and we give a precise characterization of what is needed for optimal order l2 approximation of the function and of its divergence as applications we demonstrate degradation of the convergence order on quadrilateral meshes as compared to rectangular meshes for some standard finite element approximations of h div we also derive new estimates for approximation by quadrilateral raviart thomas elements requiring less regularity and propose a new quadrilateral finite element space which provides optimal order approximation in h div finally we demonstrate the theory with numerical computations of mixed and least squares finite element approximations of the solution of poisson s equation

unrestricted complementation in language equations over a one letter alphabet recently the complete solution of systems of language equations over a one letter alphabet has been derived where the operators are union concatenation and star this paper addresses the question of adding the complementation operator it is known that if no stars are present and if the concatenation operator is restricted such equations need not have solutions but if they do they can be solved explicitly if the constants are regular in which case the solutions are also regular in this paper we study language equations over a one letter alphabet where unrestricted concatenation interacts with complementation union and star we define a procedure for determining a regular solution of the general type of equation assuming that all constants are regular discuss its properties and show examples we then prove that in general equations with complementation and complementation and concatenation in which all constants are regular may have nonregular solutions this shows that language equations can be used to obtain non context free languages from regular languages using only operators under which the regular languages are closed

on the comptational complexity of determining polyatomic structures by x rays the problem of recovering the structure of crystalline materials from their discrete x rays is of fundamental interest in many practical applications an important special case concerns determining the position of atoms of several different types in the integer lattice given the number of each type lying on each line parallel to some lattice directions we show that the corresponding consistency problem is np complete for any two or more different fixed directions when six or more types of atoms are involved

on the unique satisfiability problem unique sat is the problem of deciding whether a given boolean formula has exactly one satisfying truth assignment this problem is a typical moreover complete representative of a natural class of problems about unique solutions all these problems belong to the class dife l1 l2 l1 lz np studied by papadimitriou and yannakakis we consider the relationship between these two classes particularly whether unique sat is dife complete it is if np co np we construct an oracle relative to which unique sat is not complete for dif and another oracle relative to which unique sat is complete for dif e whereas np v co np

discontinuous galerkin approximation of the laplace eigenproblem in this paper we analyse the problem of computing eigenvalues and eigenfunctions of the laplace operator by means of discontinuous galerkin dg methods it results that several dg methods actually provide a spectrally correct approximation of the laplace operator we present here the convergence theory which applies to a wide class of dg methods as well as numerical tests demonstrating the theoretical results

unique optimal solutions complexity results for identifying and locating dominating codes abstract we investigate the complexity of four decision problems dealing with the uniqueness of a solution in a graph uniqueness of an r locating dominating code with bounded size u ldcr uniqueness of an optimal r locating dominating code u oldcr uniqueness of an r identifying code with bounded size u idcr uniqueness of an optimal r identifying code u oidcr for any fixed integer r 1 in particular we describe a polynomial reduction from unique satisfiability of a boolean formula u sat to u oldcr and from u sat to u oidcr for u ldcr and u idcr we can do even better and prove that their complexity is the same as that of u sat up to polynomials consequently all these problems are np hard and u ldcr and u idcr belong to the class dp

finite element approximation of the nonstationary navier stokes problem i regularity of solutions and second order error estimates for spatial discretization this is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary navier stokes equations second order error estimates are proven for spatial discretization using conforming or nonconforming elements the results indicate a fluid like behavior of the approximations even in the case of large data so long as the solution remains regular the analysis is based on sharp a priori estimates for the solution particularly reflecting its behavior as t to 0 and as t to infty it is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the navier stokes equations as it depends on nonlocal compatibility conditions for the data the results which are presented here are independent of such compatibility conditions which cannot be verified in practice

propositional circumscription and extended closed world reasoning are p p 2 complete abstract circumscription and the closed world assumption with its variants are well known nonmonotonic techniques for reasoning with incomplete knowledge their complexity in the propositional case has been studied in detail for fragments of propositional logic one open problem is whether the deduction problem for arbitrary propositional theories under the extended closed world assumption or under circumscription is p 2 complete i e complete for a class of the second level of the polynomial hierarchy we answer this question by proving these problems p 2 complete and we show how this result applies to other variants of closed world reasoning

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

constraint preserving schemes for some gauge invariant wave equations we study discretizations of the maxwell klein gordon equation as an example of a constrained geometric nonlinear evolution partial differential equation for the temporal gauge we propose a fully discrete scheme which preserves the nonlinear constraint thanks to a special application of lagrange multipliers we show that the method generalizes to hamiltonian wave equations whose kinetic and potential energy are both invariant under a group of transformations even though the galerkin spaces are not invariant we then extend the method to the lorenz gauge numerical results illustrate the discussion

np is as easy as detecting unique solutions abstract for every known np complete problem the number of solutions of its instances varies over a large range from zero to exponentially many it is therefore natural to ask if the inherent intractability of np complete problem is caused by this wide variation we give a negative answer to this question using the notion of randomized polynomial time reducibility we show that the problems of distinguishing between instances of sat having zero or one solution or of finding solutions to instances of sat having a unique solution are as hard as sat under randomized reductions several corollaries about the difficulty of specific problems follow for example computing the parity of the number of solutions of a sat formula is shown to be np hard and deciding if a sat formula has a unique solution is shown to be d p hard under randomized reduction central to the study of cryptography is the question as to whether there exist np problems whose instances have solutions that are unique but are hard to find our result can be interpreted as strengthening the belief that such problems exist

on the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form in the approximation of linear elliptic operators in mixed form it is well known that the so called inf sup and ellipticity in the kernel properties are sufficient and in a sense to be made precise necessary in order to have good approximation properties and optimal error bounds one might think in the spirit of mercier osborn rappaz raviart and in consideration of the good behavior of commonly used mixed elements like raviart thomas or brezzi douglas marini elements that these conditions are also sufficient to ensure good convergence properties for eigenvalues in this paper we show that this is not the case in particular we present examples of mixed finite element approximations that satisfy the above properties but exhibit spurious eigenvalues such bad behavior is proved analytically and demonstrated in numerical experiments we also present additional assumptions fulfilled by the commonly used mixed methods already mentioned which guarantee optimal error bounds for eigenvalue approximations as well

language equations with complementation decision problems systems of language equations of the form xi i x1 xn 1 i n are studied here every i may contain the operations of concatenation and complementation the properties of having solutions and of having a unique solution are given mathematical characterizations as decision problems the former is np complete while the latter is pspace hard and is in co re and its decidability remains in general open uniqueness becomes decidable in the case of a unary alphabet where it is us complete and in the case of linear concatenation where it is l complete

polynomial terse sets abstract let a be a set and k n be such that we wish to know the answers to x1 a x2 a xk a for various k tuples x1 x2 xk if this problem requires k queries to a in order to be solved in polynomial time then a is called polynomial terse or pterse we show the existence of both arbitrarily complex pterse and non pterse sets and that p np iff every np complete set is pterse we also show connections with p immunity p selective p generic sets and the boolean hierarchy in our framework unique satisfiability and a variation of it called ksat is in some sense close to satisfiability

on the computational complexity of the forcing chromatic number we consider vertex colorings of graphs in which adjacent vertices have distinct colors a graph is s chromatic if it is colorable in s colors and any coloring of it uses at least s colors the forcing chromatic number f chi g of an s chromatic graph g is the smallest number of vertices which must be colored so that with the restriction that s colors are used every remaining vertex has its color determined uniquely we estimate the computational complexity of force g relating it to the complexity class us introduced by blass and gurevich inform control 55 1982 pp 80 88 we prove that recognizing whether f chi g le2 is us hard with respect to polynomial time many one reductions moreover this problem is conp hard even under the promises that f chi g le3 and g is 3 chromatic on the other hand recognizing whether f chi g le k for each constant k is reducible to a problem in us via a disjunctive truth table reduction similar results are obtained also for forcing variants of the clique and the domination numbers of a graph

space time domain decomposition methods for diffusion problems in mixed formulations this paper is concerned with global in time nonoverlapping domain decomposition methods for the mixed formulation of the diffusion problem two approaches are considered one uses the time dependent steklov poincare operator and the other uses optimized schwarz waveform relaxation oswr based on robin transmission conditions for each method a mixed formulation of an interface problem on the space time interfaces between subdomains is derived and different time grids are employed to adapt to different time scales in the subdomains demonstrations of the well posedness of the robin subdomain problems involved in the oswr method and a convergence proof of the oswr algorithm are given for the mixed formulation numerical results for two dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods

an efficient solution methodology to study the response of a beam on viscoelastic and nonlinear unilateral foundation static response abstract many engineering materials and foundations such as soils demonstrate nonlinear and viscoelastic behaviour yet it is challenging to develop static and dynamic models of systems that include these materials and are able to predict the behaviour over a wide range of loading conditions this research is focused on a specific example a pinned pinned beam interacting with polyurethane foam foundation two cases when the foundation can react in tension and compression as well as only in compression are considered the model developed here is capable of predicting the response to static as well as dynamic forces whether concentrated or distributed galerkin s method is used to derive modal amplitude equations in the tensionless foundation case the contact region changes with beam motion and the estimation of the co ordinates of the lift off points is embedded into the solution procedure an efficient solution technique is proposed that is capable of handling cases where there are multiple contact and non contact regions depending on the loading profiles a high number of modes may need to be included in the solution and to speed up computation time a convolution method is used to evaluate the integral terms in the model the adaptability of the solution scheme to complicated loading patterns is demonstrated via examples the solution approach proposed is applicable to dynamic loadings as well and in these cases the automated treatment of complicated response patterns makes the convolution approach particularly attractive the influence of various parameters on the static response is discussed

on the expressive power of univariate equations over sets of natural numbers equations of the form email protected x are considered where the unknown x is a set of natural numbers the expression f x may contain the operations of set addition defined as s t m n email protected s email protected t union intersection as well as ultimately periodic constants an equation with a non periodic solution of exponential growth rate is constructed at the same time it is demonstrated that no sets with super exponential growth rate can be represented it is also shown that restricted classes of these equations cannot represent sets with super linearly growing complements nor sets that are additive bases of order 2 the results have direct implications on the power of unary conjunctive grammars with one nonterminal symbol

complexity and expressive power of deterministic semantics for datalog abstract deterministic models are partial stable models which are not contradicted by any other stable model i e m is a deterministic model if there is no stable model n such that m n is not an interpretation for instanced the well founded model which coincides with the intersection of all partial stable models is a deterministic model as the well founded model is deterministic and unique for each program well founded model semantics has been proposed as the canonical deterministic semantics for partial stable models but the well founded model is not the unique deterministic model indeed the family of deterministic partial stable models is not in general a singleton and admits a minimum the well founded model and a maximum the max deterministic model the latter model is another candidate for a deterministic semantics the aim of this paper is to study the complexity and the expressive power of deterministic semantics in coherence with the deterministic nature of the model the expressive power of max deterministic semantics is shown to be able to express problems with unique solutions whereas the well founded model only captures a proper subset of the queries computable in polynomial time the so called fixpoint queries

the complexity of very simple boolean formulas with applications the concepts of textbf sat hardness and textbf sat completeness modulo npolylogn time and linear size reducibility denoted by textbf sat hard npolylogn n and textbf sat complete npolylogn n respectively are introduced regardless of whether textbf p textbf np or textbf p neq textbf np it is shown that intuitivelyeach textbf sat hard npolylogn n problem requires essentially at least as much deterministic time as andeach textbf sat complete npolylogn n problem requires essentially the same deterministic time as the satisfiability problem for 3cnf formulas it is proved that the leqq satisfiability tautology unique satisfiability equivalence and minimization problems are already textbf sat complete npolylogn n for very simple boolean formulas and for very simple systems of boolean equations these completeness results are used to characterize the deterministic time complexities of a number of problems for lattices propositional calculi

set constraints in some equational theories set constraints are relations between sets of ground terms over a given alphabet they give a natural formalism for many problems in program analysis type inference order sorted unification and constraint logic programming in this paper we start studies of set constraints in the environment given by equational specifications we show that in the case of associativity i e in free monoids as well as in the case of associativity and commutativity i e in commutative monoids the problem of consistency of systems of set constraints is undecidable in linear nonerasing shallow theories the consistency of systems of positive set constraints is nexptime complete and in linear shallow theories the problem for positive and negative set constraints is decidable

complexity of unique list colorability given a list l v for each vertex v we say that the graph g is l colorable if there is a proper vertex coloring of g where each vertex v takes its color from l v the graph is uniquelyk list colorable if there is a list assignment l such that l v k for every vertex v and the graph has exactly one l coloring with these lists mahdian and mahmoodian m mahdian e s mahmoodian a characterization of uniquely 2 list colorable graphs ars combin 51 1999 295 305 gave a polynomial time characterization of uniquely 2 list colorable graphs answering an open question from m ghebleh e s mahmoodian on uniquely list colorable graphs ars combin 59 2001 307 318 m mahdian e s mahmoodian a characterization of uniquely 2 list colorable graphs ars combin 51 1999 295 305 we show that uniquely 3 list colorable graphs are unlikely to have such a nice characterization since recognizing these graphs is s 2 p complete

separating complexity classes with tally oracles abstract long and selman 1986 proved that for most familiar pairs of complexity classes separating the classes with a tally oracle is no easier than truly separating the classes refuting a claim in the literature we prove for the first time that for many familiar pairs of complexity classes separating the classes with a tally oracle is easier than truly separating the classes

on the power of two way random generators and the impossibility of deterministic poly space simulations borodin cook and pippenger inform and control 58 1983 96 114 proved that both probabilistic acceptors and transducers working in space s n log n can be simulated by deterministic machines in o s n 2 space the definition of probabilistic computations uses one way read only random tape borodin et al asked is it possible to extend our simulation results to the case of a two way read only oracle head in the same vein furst lipton and stockmeyer inform and control 64 1985 43 51 suggested that it could be a difference between two way and one way random tape for space bounded probabilistic computations where the space bound is much less than the length of y it could matter y denoting the random tape inscription in this paper we give a full characterization of two way random space classes that answers both questions karpinski and verbeek there is no polynomial deterministic space simulation of probabilistic space with two way random tape generator inform and control 67 1985 158 162 proved that there is no polynomial deterministic space simulation of two way random space without giving any recursive upper bound the results of this paper solved the open questions of karpinski and verbeek 1985 karpinski and verbeek 1985 and gave full characterization in sense of upper and lower deterministic space classes they are proved precisely exponentially more powerful than the corresponding one way classes

lower bounds and the hardness of counting properties rice s theorem states that all nontrivial language properties of recursively enumerable sets are undecidable borchert and stephan math logic quart 46 4 2000 489 504 started the search for complexity theoretic analogs of rice s theorem and proved that every nontrivial counting property of boolean circuits is up hard hemaspaandra and rothe theoret comput sci 244 1 2 2000 205 217 improved the up hardness lower bound to upo 1 hardness the present paper raises the lower bound for nontrivial counting properties from upo 1 hardness to fewp hardness i e from constant ambiguity nondeterminism to polynomial ambiguity nondeterminism furthermore we prove that no relativizable technique can raise this lower bound to fewp 1 ttp hardness we also prove a rice style theorem for np namely that every nontrivial language property of np sets is np hard and for a broad class of leaf language classes we prove a sufficient condition for the natural analog of rice s theorem to hold

space time domain decomposition and mixed formulation for solving reduced fracture models in this paper we are interested in the fast path fracture and we aim to use global in time nonoverlapping domain decomposition methods to model flow and transport problems in a porous medium containing such a fracture we consider a reduced model in which the fracture is treated as an interface between the two subdomains two domain decomposition methods are considered one uses the time dependent steklovpoincare operator and the other uses optimized schwarz waveform relaxation oswr based on ventcell transmission conditions for each method a mixed formulation of an interface problem on the space time interface is derived and different time grids are employed to adapt to different time scales in the subdomains and in the fracture demonstrations of the well posedness of the ventcell subdomain problems is given for the mixed formulation an analysis for the convergence factor of the oswr algorithm is given in the case with fractures to compute the optimized parameters numerical results for two dimensional problems with strong heterogeneities are presented to illustrate the performance of the two methods