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Carsten Carstensen - One of the best experts on this subject based on the ideXlab platform.

  • residual based a Posteriori Error Estimate for a mixed reiβner mindlin plate finite element method
    Numerische Mathematik, 2006
    Co-Authors: Carsten Carstensen, Joachim Schoberl
    Abstract:

    Reliable and efficient residual-based a Posteriori Error Estimates are established for the stabilised locking-free finite element methods for the Reissner-Mindlin plate model. The Error is Estimated by a computable Error estimator from above and below up to multiplicative constants that do neither depend on the mesh-size nor on the plate's thickness and are uniform for a wide range of stabilisation parameter. The Error is controlled in norms that are known to converge to zero in a quasi-optimal way. An adaptive algorithm is suggested and run for improving the convergence rates in three numerical examples for thicknesses 0.1, .001 and .001.

  • Residual-based a Posteriori Error Estimate for a mixed Reißner-Mindlin plate finite element method
    Numerische Mathematik, 2006
    Co-Authors: Carsten Carstensen, Joachim Schoberl
    Abstract:

    Reliable and efficient residual-based a Posteriori Error Estimates are established for the stabilised locking-free finite element methods for the Reissner-Mindlin plate model. The Error is Estimated by a computable Error estimator from above and below up to multiplicative constants that do neither depend on the mesh-size nor on the plate's thickness and are uniform for a wide range of stabilisation parameter. The Error is controlled in norms that are known to converge to zero in a quasi-optimal way. An adaptive algorithm is suggested and run for improving the convergence rates in three numerical examples for thicknesses 0.1, .001 and .001.

  • residual based a Posteriori Error Estimate for a mixed reisner mindlin plate finite
    2006
    Co-Authors: Carsten Carstensen, Joachim Schoberl
    Abstract:

    Reliable and efficient residual-based a Posteriori Error Estimates are established for the stabilised locking-free finite element methods for the Reiss- ner-Mindlin plate model. The Error is Estimated by a computable Error estimator from above and below up to multiplicative constants that do neither depend on the mesh-size nor on the plate's thickness and are uniform for a wide range of sta- bilisation parameter. The Error is controlled in norms that are known to converge to zero in a quasi-optimal way. An adaptive algorithm is suggested and run for improving the convergence rates in three numerical examples for thicknesses 0.1, .001 and .001.

  • Residual-based a Posteriori Error Estimate for hypersingular equation on surfaces
    Numerische Mathematik, 2004
    Co-Authors: Carsten Carstensen, Matthias Maischak, D Praetorius, E.p. Stephan
    Abstract:

    The hypersingular integral equation of the first kind equivalently describes screen and Neumann problems on an open surface piece. The paper establishes a computable upper Error bound for its Galerkin approximation and so motivates adaptive mesh refining algorithms. Numerical experiments for triangular elements on a screen provide empirical evidence of the superiority of adapted over uniform mesh-refining. The numerical realisation requires the evaluation of the hypersingular integral operator at a source point; this and other details on the algorithm are included.

  • a Posteriori Error Estimate and h adaptive algorithm on surfaces for symm s integral equation
    Numerische Mathematik, 2001
    Co-Authors: Carsten Carstensen, Matthias Maischak, Ernst P. Stephan
    Abstract:

    A residual-based a Posteriori Error Estimate for boundary integral equations on surfaces is derived in this paper. A localisation argument involves a Lipschitz partition of unity such as nodal basis functions known from finite element methods. The abstract Estimate does not use any property of the discrete solution, but simplifies for the Galerkin discretisation of Symm's integral equation if piecewise constants belong to the test space. The Estimate suggests an isotropic adaptive algorithm for automatic mesh-refinement. An alternative motivation from a two-level Error Estimate is possible but then requires a saturation assumption. The efficiency of an anisotropic version is discussed and supported by numerical experiments.

Ernst P. Stephan - One of the best experts on this subject based on the ideXlab platform.

  • A residual a Posteriori Error Estimate for the time–domain boundary element method
    Numerische Mathematik, 2020
    Co-Authors: Heiko Gimperlein, Ceyhun Özdemir, David Stark, Ernst P. Stephan
    Abstract:

    This article investigates residual a Posteriori Error Estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable Estimates for Dirichlet and acoustic boundary conditions which hold for a large class of discretizations. Efficiency of the Error Estimate is shown for a natural discretization of low order. Numerical examples confirm the theoretical results. The resulting adaptive mesh refinement procedures in 3 d recover the adaptive convergence rates known for elliptic problems.

  • A residual a Posteriori Error Estimate for the time-domain boundary element method
    Numerische Mathematik, 2020
    Co-Authors: Heiko Gimperlein, David Stark, Ceyhun Oezdemir, Ernst P. Stephan
    Abstract:

    This article investigates residual a Posteriori Error Estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable Estimates for Dirichlet and acoustic boundary conditions which hold for a large class of discretizations. Efficiency of the Error Estimate is shown for a natural discretization of low order. Numerical examples confirm the theoretical results. The resulting adaptive mesh refinement procedures in 3d recover the adaptive convergence rates known for elliptic problems.

  • A HIERARCHICAL A Posteriori Error Estimate FOR AN ADVECTION-DIFFUSION-REACTION PROBLEM
    Mathematical Models and Methods in Applied Sciences, 2005
    Co-Authors: Rodolfo Araya, Abner H. Poza, Ernst P. Stephan
    Abstract:

    In this work we introduce a new a Posteriori Error Estimate of hierarchical type for the advection-diffusion-reaction equation. We prove the equivalence between the energy norm of the Error and our Error Estimate using an auxiliary linear problem for the residual and an easy way to prove inf–sup condition.

  • A mixed finite element method for nonlinear elasticity: two-fold saddle point approach and a-Posteriori Error Estimate
    Numerische Mathematik, 2002
    Co-Authors: Mauricio A. Barrientos, Gabriel N. Gatica, Ernst P. Stephan
    Abstract:

    We extend the applicability of stable mixed finite elements for linear plane elasticity, such as PEERS, to a mixed variational formulation of hyperelasticity. The present approach is based on the introduction of the strain tensor as a further unknown, which yields a two-fold saddle point nonlinear operator equation for the corresponding weak formulation. We provide the uniqueness of solution for the continuous and discrete schemes, and derive the usual Cea Estimate for the associated Error. Finally, a reliable a-Posteriori Error Estimate, based on the solution of local Dirichlet problems, and well suited for adaptive computations, is also given.

  • a Posteriori Error Estimate and h adaptive algorithm on surfaces for symm s integral equation
    Numerische Mathematik, 2001
    Co-Authors: Carsten Carstensen, Matthias Maischak, Ernst P. Stephan
    Abstract:

    A residual-based a Posteriori Error Estimate for boundary integral equations on surfaces is derived in this paper. A localisation argument involves a Lipschitz partition of unity such as nodal basis functions known from finite element methods. The abstract Estimate does not use any property of the discrete solution, but simplifies for the Galerkin discretisation of Symm's integral equation if piecewise constants belong to the test space. The Estimate suggests an isotropic adaptive algorithm for automatic mesh-refinement. An alternative motivation from a two-level Error Estimate is possible but then requires a saturation assumption. The efficiency of an anisotropic version is discussed and supported by numerical experiments.

A Borio - One of the best experts on this subject based on the ideXlab platform.

  • Anisotropic a Posteriori Error Estimate for the virtual element method
    IMA Journal of Numerical Analysis, 2021
    Co-Authors: P F Antonietti, S Berrone, A Borio, A D’auria, M Verani, S Weisser
    Abstract:

    Abstract We derive an anisotropic a Posteriori Error Estimate for the adaptive conforming virtual element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its approximation results to prove the reliability of the Error indicator. We design and implement the corresponding adaptive polygonal anisotropic algorithm. Several numerical tests assess the superiority of the proposed algorithm in comparison with standard polygonal isotropic mesh refinement schemes.

  • A residual a Posteriori Error Estimate for the Virtual Element Method
    Mathematical Models and Methods in Applied Sciences, 2017
    Co-Authors: S Berrone, A Borio
    Abstract:

    A residual-based a Posteriori Error Estimate for the Poisson problem with discontinuous diffusivity coefficient is derived in the case of a virtual element discretization. The Error is measured considering a suitable polynomial projection of the discrete solution to prove an equivalence between the defined Error and a computable residual based Error estimator that does not involve any term related to the virtual element stabilization. Numerical results display a very good behavior of the ratio between the Error and the Error estimator, resulting independent of the meshsize and element distortion.

  • a Posteriori Error Estimate for a pde constrained optimization formulation for the flow in dfns
    SIAM Journal on Numerical Analysis, 2016
    Co-Authors: S Berrone, A Borio, Stefano Scialo
    Abstract:

    Flows in fractured media have been modeled with many different approaches in order to get reliable and efficient simulations for many critical applications. The common issues to be tackled are the wide range of scales involved in the phenomenon, the complexity of the domain, and the huge computational cost. In this paper we introduce residual-based “a Posteriori” Error Estimates for a formulation of the flow in the discrete fracture networks based on a constrained optimization approach (see Berrone, Pieraccini, and Scialo [SIAM J. Sci. Comput., 35 (2013), pp. B487--B510], [SIAM J. Sci. Comput., 35 (2013), pp. A908--A935], [J. Comput. Phys., 256 (2014), pp. 838--853]), suitable to overcome all the difficulties related to a good quality mesh generation with conformity requirement.

Joachim Schoberl - One of the best experts on this subject based on the ideXlab platform.

  • residual based a Posteriori Error Estimate for a mixed reiβner mindlin plate finite element method
    Numerische Mathematik, 2006
    Co-Authors: Carsten Carstensen, Joachim Schoberl
    Abstract:

    Reliable and efficient residual-based a Posteriori Error Estimates are established for the stabilised locking-free finite element methods for the Reissner-Mindlin plate model. The Error is Estimated by a computable Error estimator from above and below up to multiplicative constants that do neither depend on the mesh-size nor on the plate's thickness and are uniform for a wide range of stabilisation parameter. The Error is controlled in norms that are known to converge to zero in a quasi-optimal way. An adaptive algorithm is suggested and run for improving the convergence rates in three numerical examples for thicknesses 0.1, .001 and .001.

  • Residual-based a Posteriori Error Estimate for a mixed Reißner-Mindlin plate finite element method
    Numerische Mathematik, 2006
    Co-Authors: Carsten Carstensen, Joachim Schoberl
    Abstract:

    Reliable and efficient residual-based a Posteriori Error Estimates are established for the stabilised locking-free finite element methods for the Reissner-Mindlin plate model. The Error is Estimated by a computable Error estimator from above and below up to multiplicative constants that do neither depend on the mesh-size nor on the plate's thickness and are uniform for a wide range of stabilisation parameter. The Error is controlled in norms that are known to converge to zero in a quasi-optimal way. An adaptive algorithm is suggested and run for improving the convergence rates in three numerical examples for thicknesses 0.1, .001 and .001.

  • residual based a Posteriori Error Estimate for a mixed reisner mindlin plate finite
    2006
    Co-Authors: Carsten Carstensen, Joachim Schoberl
    Abstract:

    Reliable and efficient residual-based a Posteriori Error Estimates are established for the stabilised locking-free finite element methods for the Reiss- ner-Mindlin plate model. The Error is Estimated by a computable Error estimator from above and below up to multiplicative constants that do neither depend on the mesh-size nor on the plate's thickness and are uniform for a wide range of sta- bilisation parameter. The Error is controlled in norms that are known to converge to zero in a quasi-optimal way. An adaptive algorithm is suggested and run for improving the convergence rates in three numerical examples for thicknesses 0.1, .001 and .001.

Natalia Kopteva - One of the best experts on this subject based on the ideXlab platform.