[en] A rigorous approach is presented to the design and evaluation of oscillation-free, semidiscrete approximations to discontinuous solutions of conservation laws. This approach draws on properties of extrema in the exact solution in order to derive optimal conditions with such attributes as: (1) no effects on steady extrema; (2) the creation of a wavelength-dependent second-order error at moving extrema; (3) the possibility of extension to vector problems; and (4) the possibility of extension to multidimensions without loss of accuracy. The approach also provides a simple conceptual framework for reassessing the significance and effects of TVD and related conditions. 29 refs

[en] The mixed Petrov-Galerkin method is applied to axisymmetric shells with uniform and non uniform meshes. Numerical experiments with a cylindrical shell showed a significant improvement in convergence and accuracy with adaptive meshes. (A.C.A.S.)

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[en] A modified Newton method for unconstrained minimization is presented and analysed. The modification is based upon the model trust region approach. This report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified Newton iteration. Several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis. Very strong convergence results are presented concerning the minimization algorithm. In particular, the explicit use of second order information is justified by demonstrating that the iterates converge to a point which satisfies the second order necessary conditions for minimization. With the exception of very pathological cases this occurs whenever the algorithm is applied to problems with continuous second partial derivatives

[en] A coarse-mesh method is described which is characterized by dividing the space into rectangular boxes and by the assumption that along an edge of a box the sum of the transversal leakages will be approximated by a straight line. Compared with common difference methods the necessary computing time is reduced for 2-d problems by a factor of about 10 and for 3-d problems by a factor of about 10 and for 3-d problems by an estimated factor of about 30. This method requires a measure of understanding of the calculation by the user. (orig.)

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[en] We study generalizations of Newton's method which terminate quadratically under adequate conditions and are occasionally faster than the standard Newton schemes. These methods also apply to problems involving functions which are not sufficiently regular to allow for the application of the classical method of Newton. In particular, the generalized schemes can be used to solve variational inequalities. Numerical examples are given. (author). 13 refs

[en] Computer aided symbolic manipulation has previously been used in studies of weakly nonlinear behavior in plasmas. The application of such symbolic manipulation techniques to the study of the stability of a specific finite difference scheme is investigated. Eigenvalue calculations for the Von Neumann matrix are described

[en] In this paper a new finite element model is constructed combining an r- refinement scheme with the CCAU method. The new formulation gives better approximation for boundary and internal layers compared to the standard CCAU, without increasing computer codes. (author)