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  • Articles  (9)
  • Mathematics Subject Classification (1991):65N30  (9)
  • Springer  (9)
  • American Geophysical Union (AGU)
  • Annual Reviews
  • 1995-1999  (9)
  • 1980-1984
  • 1935-1939
  • 1995  (9)
  • Mathematics  (9)
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  • Articles  (9)
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  • Springer  (9)
  • American Geophysical Union (AGU)
  • Annual Reviews
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  • 1995-1999  (9)
  • 1980-1984
  • 1935-1939
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  • Mathematics  (9)
  • 1
    Electronic Resource
    Electronic Resource
    Bounds on spectral condition numbers of matrices arising in the $p$ -version of the finite element method (1995)
    Springer
    Numerische Mathematik 69 (1995), S. 333-352 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We estimate condition numbers of $p$ -version matrices for tensor product elements with two choices of reference element degrees of freedom. In one case (Lagrange elements) the condition numbers grow exponentially in $p$ , whereas in the other (hierarchical basis functions based on Tchebycheff polynomials) the condition numbers grow rapidly but only algebraically in $p$ . We conjecture that regardless of the choice of basis the condition numbers grow like $p^{4d}$ or faster, where $d$ is the dimension of the spatial domain.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050096
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  • 2
    Electronic Resource
    Electronic Resource
    Parallel algorithms for maximal monotone operators of local type (1995)
    Springer
    Numerische Mathematik 71 (1995), S. 29-58 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. This paper presents general algorithms for the parallel solution of finite element problems associated with maximal monotone operators of local type. The latter concept, which is also introduced here, is well suited to capture the idea that the given operator is the discretization of a differential operator that may involve nonlinearities and/or constraints as long as those are of a local nature. Our algorithms are obtained as a combination of known algorithms for possibly multi-valued maximal monotone operators with appropriate decompositions of the domain. This work extends a method due to two of the authors in the single-valued and linear case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050135
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  • 3
    Electronic Resource
    Electronic Resource
    Mixed finite element approximation of a degenerate elliptic problem (1995)
    Springer
    Numerische Mathematik 71 (1995), S. 225-236 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We present a mixed finite element approximation of an elliptic problem with degenerate coefficients, arising in the study of the electromagnetic field in a resonant structure with cylindrical symmetry. Optimal error bounds are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050142
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  • 4
    Electronic Resource
    Electronic Resource
    The maximum angle condition in the finite element method for monotone problems with applications in magnetostatics (1995)
    Springer
    Numerische Mathematik 71 (1995), S. 399-417 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. The finite element method for an elliptic equation with discontinuous coefficients (obtained for the magnetic potential from Maxwell's equations) is analyzed in the union of closed domains the boundaries of which form a system of three circles with the same centre. As the middle domain is very narrow the triangulations obeying the maximum angle condition are considered. In the case of piecewise linear trial functions the maximum rate of convergence $O(h)$ in the norm of the space $H^1(\Omega_h)$ is proved under the following conditions: 1. the exact solution $u\in H^1(\Omega)$ is piecewise of class $H^2$ ; 2. the family of subtriangulations $\{{\cal T}_h^{\rm A}\}$ of the narrow subdomain $\Omega^{\rm A}$ satisfies the maximum angle condition expressed by relation (38). The paper extends the results of [24].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050151
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  • 5
    Electronic Resource
    Electronic Resource
    The interpolation theorem for narrow quadrilateral isoparametric finite elements (1995)
    Springer
    Numerische Mathematik 72 (1995), S. 123-141 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. The interpolation theorem for convex quadrilateral isoparametric finite elements is proved in the case when the condition $\varrho_K/h_K\ge\varrho_0〉0$ is not satisfied, where $h_K$ is the diameter of the element $K$ and $\varrho_K$ is the radius of an inscribed circle in $K$ . The interpolation error is $O(h_K^2)$ in the $L_2(K)$ -norm and $O(h_K)$ in the $H^1(K)$ -norm provided that the interpolated function belongs to $H^2(K)$ . In the case when the long sides of the quadrilateral $K$ are parallel the constants appearing in the estimates are evaluated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050163
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  • 6
    Electronic Resource
    Electronic Resource
    Convergence of a finite element method for non-parametric mean curvature flow (1995)
    Springer
    Numerische Mathematik 72 (1995), S. 197-222 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. Convergence for the spatial discretization by linear finite elements of the non-parametric mean curvature flow is proved under natural regularity assumptions on the continuous solution. Asymptotic convergence is also obtained for the time derivative which is proportional to mean curvature. An existence result for the continuous problem in adequate spaces is included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050166
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  • 7
    Electronic Resource
    Electronic Resource
    On a decoupled algorithm for solving a finite element problem for the approximation of viscoelastic fluid flow (1995)
    Springer
    Numerische Mathematik 72 (1995), S. 223-238 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. The aim of this work is to study a decoupled algorithm of a fixed point for solving a finite element (FE) problem for the approximation of viscoelastic fluid flow obeying an Oldroyd B differential model. The interest for this algorithm lies in its applications to numerical simulation and in the cost of computing. Furthermore it is easy to bring this algorithm into play. The unknowns are $\sigma$ the viscoelastic part of the extra stress tensor, $u$ the velocity and $p$ the pressure. We suppose that the solution $(\sigma,u,p)$ is sufficiently smooth and small. The approximation of stress, velocity and pressure are resp. $P_1$ discontinuous, $P_2$ continuous, $P_1$ continuous FE. Upwinding needed for convection of $\sigma$ , is made by discontinuous FE. The method consists to solve alternatively a transport equation for the stress, and a Stokes like problem for velocity and pressure. Previously, results of existence of the solution for the approximate problem and error bounds have been obtained using fixed point techniques with coupled algorithm. In this paper we show that the mapping of the decoupled fixed point algorithm is locally (in a neighbourhood of $(\sigma,u,p)$ ) contracting and we obtain existence, unicity (locally) of the solution of the approximate problem and error bounds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050167
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  • 8
    Electronic Resource
    Electronic Resource
    Substructuring preconditioners for the $Q_1$ mortar element method (1995)
    Springer
    Numerische Mathematik 71 (1995), S. 419-449 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. The $Q_1$ mortar element method is a non conforming finite element method with $Q_1$ elements based on domain decomposition. For the Laplace equation, it yields an ill conditioned linear system. For solving the linear system, the so called preconditioned conjugate gradient method in a subspace is used. Preconditioners are proposed, and estimates on condition numbers and arithmetical complexity are given. Finally, numerical experiments are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050152
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  • 9
    Electronic Resource
    Electronic Resource
    Wavelet solutions for the Dirichlet problem (1995)
    Springer
    Numerische Mathematik 70 (1995), S. 379-396 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. A modified classical penalty method for solving a Dirichlet boundary value problem is presented. This new fictitious domain penalty method eliminates the traditional need of generating a complex computation grid in the case of irregular domains. It is based on the fact that one can expand the boundary measure under the chosen basis which leads to a fast, approximate calculation of boundary integral. The compact support and orthonormality of the basis are essential for representing the boundary measure numerically, and therefore for implementing this methodology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050125
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