• Presentation Name4️⃣: Finite elements approximation of second order linear elliptic equations
    Presenter: Professor Francois Murat
    Date: 2010-11-05
    Location: 光华东主楼1801
    Abstract🦶🏽:

    In this lecture I will report on joint work with J. Casado-Diaz, T.
    Chacon Rebollo, V. Girault and M. Gomez Marmol.
    We consider, in dimension $d/ge 2$, the standard $P 1$ finite elements
    approximation of the second order linear elliptic equation in divergence
    form with coefficients in $L^/infty(/Omega)$ which generalizes Laplace's
    equation. We assume that the family of triangulations is regular and
    that it satisfies an hypothesis close to the classical hypothesis which
    implies the discrete maximum principle. When the right-hand side belongs
    to $L^1(/Omega)$, we prove that the unique solution of the discrete
    problem converges in $W^{1,q}_0(/Omega)$ (for every $q$ with
    $/displaystyle{1 /leq q<{d /over d-1}})$ to the unique renormalized
    solution of the problem. We obtain a weaker result when the right-hand
    side is a bounded Radon measure. In the case where the dimension is
    $d=2$ or $d=3$ and where the coefficients are smooth, we give an
    error estimate in $W^{1,q}_0(/Omega)$ when the right-hand side belongs
    to $L^r(/Omega)$ for some $r>1$.


     

    Annual Speech Directory: No.94

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