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1 Superconvergent discontinuous Galerkin methods for second-order elliptic problems / A multiscale finite element method for partial differential equations posed in domains with rough boundaries / Alexandre L. Madureira 35 Convergence and optimality of adaptive mixed finite element methods / 79 Overlapping additive Schwarz preconditioners for elliptic PDEs(More)
We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a p-adic factorization method based on Newton polygons of higher order. The running-time and memory requirements of the algorithm appear to be very good: for a given prime number p, it computes the p-valuation of the(More)
Let K be the number field determined by a monic irreducible polynomial f (x) with integer coefficients. In previous papers we parameterized the prime ideals of K in terms of certain invariants attached to Newton polygons of higher order of f (x). In this paper we show how to carry out the basic operations on fractional ideals of K in terms of these(More)
Let f (x) be a separable polynomial over a local field. Montes algorithm computes certain approximations to the different irreducible factors of f (x), with strong arithmetic properties. In this paper we develop an algorithm to improve any one of these approximations , till a prescribed precision is attained. The most natural application of this "(More)