TY - JOUR T1 - A finite element approximation of the Griffith\\\'s model in fracture mechanics JF - Numer. Math., 2003, 95, 653 Y1 - 2003 A1 - Matteo Negri AB - The Griffith model for the mechanics of fractures in brittle materials is consider in the weak formulation of SBD spaces. We suggest an approximation, in the sense of Gamma-convergence, by a sequence of discrete functionals defined on finite elements spaces over structured and adaptive triangulations. The quasi-static evolution for boundary value problems is also taken into account and some numerical results are shown. PB - SISSA Library UR - http://hdl.handle.net/1963/1548 U1 - 2570 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Linearized elasticity as gamma-limit of finite elasticity JF - Set-Valued Anal. 10 (2002), p.165-183 Y1 - 2002 A1 - Gianni Dal Maso A1 - Matteo Negri A1 - Danilo Percivale PB - Springer UR - http://hdl.handle.net/1963/3052 U1 - 1281 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Numerical Methods for Free-Discontinuity Problems Based on Approximations by Γ-Convergence Y1 - 2001 A1 - Matteo Negri KW - Mumford-Shah functional PB - SISSA UR - http://hdl.handle.net/1963/5399 U1 - 5226 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Numerical minimization of the Mumford-Shah functional JF - Calcolo, 2001, 38, 67 Y1 - 2001 A1 - Matteo Negri A1 - Maurizio Paolini PB - SISSA Library UR - http://hdl.handle.net/1963/1461 U1 - 3079 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The anisotropy introduced by the mesh in the finite element approximation of the Mumford-Shah functional JF - Numer. Funct. Anal. Optim. 20 (1999), no. 9-10, 957-982 Y1 - 1999 A1 - Matteo Negri AB - We compute explicitly the anisotropy effect in the H1 term, generated in the approximation of the Mumford-Shah functional by finite element spaces defined on structured triangulations. PB - Taylor and Francis UR - http://hdl.handle.net/1963/1276 U1 - 3179 U2 - Mathematics U3 - Functional Analysis and Applications ER -