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Computation of Singularities Coefficients for Bilaplacian Operator in a Domain with Corner

This work consists to the computation of singularities coefficients in a non convex plane domain; using a mixed finite element method of $C^0$ class based on a technical caraterisation of dual singular functions. Indeed, these coefficients are obtained directly by dual singular functions. The operator which is used in the problem is the bilaplacian involved in the problem $\Delta^2 u = f$ decomposed in two laplacians $-\Delta u = y$ and $-\Delta y = f$. Throughout the discretization, the singular functions are no longer set up on $u$ but on $y$. In some regularity conditions, the error estimations for the singular coefficients with these hypotheses, gives us an error $O(h^2 )$ when one uses dual singular functions.\\ Numerical tests with Free-fem++ allowed us to calculate and plot the curves of the coefficients of singularities by direct calculations and approximations using finite elements mixed in the same benchmark. Thus, it follows asymptotically that the gap between the two curves is very \og small \fg narrows and stabilizes when the mesh becomes more refined.}

Auteur(s) : Cheikh Seck
Pages : 71-101
Année de publication : 2018
Revue : Journal of Mathematical Sciences: Advances and Applications
N° de volume : 50
Type : Article
Mise en ligne par : SECK Cheikh