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  • 1
    Electronic Resource
    Electronic Resource
    A residual based error estimator for mortar finite element discretizations (1999)
    Springer
    Numerische Mathematik 84 (1999), S. 143-171 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N15, 65N30, 65N50, 65N55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. A residual based error estimator for the approximation of linear elliptic boundary value problems by nonconforming finite element methods is introduced and analyzed. In particular, we consider mortar finite element techniques restricting ourselves to geometrically conforming domain decomposition methods using P1 approximations in each subdomain. Additionally, a residual based error estimator for Crouzeix-Raviart elements of lowest order is presented and compared with the error estimator obtained in the more general mortar situation. It is shown that the computational effort of the error estimator can be considerably reduced if the special structure of the Lagrange multiplier is taken into account.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050467
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    Paper (German National Licenses)
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  • 2
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    Efficient parameter estimation for a methane hydrate model with active subspaces (2019)
    Springer
    In:  Computational Geosciences, 23 (2). pp. 355-372.
    Details
    Publication Date: 2022-01-31
    Description: Methane gas hydrates have increasingly become a topic of interest because of their potential as a future energy resource. There are significant economical and environmental risks associated with extraction from hydrate reservoirs, so a variety of multiphysics models have been developed to analyze prospective risks and benefits. These models generally have a large number of empirical parameters which are not known a priori. Traditional optimization-based parameter estimation frameworks may be ill-posed or computationally prohibitive. Bayesian inference methods have increasingly been found effective for estimating parameters in complex geophysical systems. These methods often are not viable in cases of computationally expensive models and high-dimensional parameter spaces. Recently, methods have been developed to effectively reduce the dimension of Bayesian inverse problems by identifying low-dimensional structures that are most informed by data. Active subspaces is one of the most generally applicable methods of performing this dimension reduction. In this paper, Bayesian inference of the parameters of a state-of-the-art mathematical model for methane hydrates based on experimental data from a triaxial compression test with gas hydrate-bearing sand is performed in an efficient way by utilizing active subspaces. Active subspaces are used to identify low-dimensional structure in the parameter space which is exploited by generating a cheap regression-based surrogate model and implementing a modified Markov chain Monte Carlo algorithm. Posterior densities having means that match the experimental data are approximated in a computationally efficient way.
    Type: Article , PeerReviewed , info:eu-repo/semantics/article
    Format: text
    DOI: 10.1007/s10596-018-9769-x
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    OceanRep: Article in a Scientific Journal - peer-reviewed
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