Ariel L. Lombardi

Mathematics Professor and Researcher

• Adjoint Professor at FCEIA, Universidad Nacional de Rosario
• Researcher of CONICET, Argentina

Research interests

• Finite element methods for partial differential equations: approximations of boundary layers, elliptic equations on polyhedra with vertex and edge singularities, elliptic equations on cusps
• Finite element methods with anisotropic meshes: interpolation error estimates
• Analysis on non-smooth domains

Publications

• M. Barrios, A.L. Lombardi, C. Penessi A finite element discretization of fractional problems using graded meshes. Preprint (in revision) 2024
• M.G. Armentano, A.L. Lombardi, C. Penessi A finite element analysis in balanced norms for a coupled system of singularly perturbed reaction-diffusion equations. Computational Methods in Applied Mathematics, to appear 2024
• M.G. Armentano, A.L. Lombardi, C. Penessi Robust Estimates in Balanced Norms for Singularly Perturbed Reaction Diffusion Equations Using Graded Meshes. Journal of Scientific Computing (2023) 96:18 doi: 10.1007/s10915-023-02245-y. View in Springer Nature SharedIt
• R.G. Durán, L. Gastaldi, A.L. Lombardi Analysis of finite element approximations of Stokes equations with non-smooth data. SIAM J. Numer. Anal. 58#6 (2020) 3309-3331. arXiv:1912.04962 [math.NA].
• M.G. Armentano, A.L. Lombardi. The Steklov eigenvalue problem in a cuspidal domain. Numer. Math. 144#2 (2020) 237-270.
• A.B. Jawtuschenko, A.L. Lombardi. A mixed discretization of elliptic problems on polyhedra using anisotropic hybrid meshes. Calcolo 56#2: 10 (2019). Preprint
• R.A. Bustinza, A.L. Lombardi, M. Solano. An anisotropic a priori error analysis for a convection–dominated diffusion problem using the HDG method. Computer Methods in Applied Mechanics and Engineering, 345#1 (2019) 382-401.
• Thomas Apel, Ariel L. Lombardi, Max Winkler. Anisotropic mesh refinement in polyhedral domains: Error estimates with data in L²(Ω). ESAIM Math. Model. Numer. Anal. 48 (2014) 1117-1145.
• Blanca Ayuso de Dios, Ariel L. Lombardi, Paola Pietra, Ludmil Zikatanov. A Block Solver for the Exponentially Fitted IIPG-0 method. R. Bank et al. (eds.). Domain Decomposition Methods in Science and Engineering XX, Lecture Notes in Computational Science and Engineering. Springer-Verlag, Berlin. 91 (2013) 239–246.
• Ricardo G. Durán, Ariel L. Lombardi, Mariana I. Prieto. Superconvergence on graded meshes for Q₁ -finite element approximation of a reaction-diffusion equation. J. Comput. Appl. Math. 242 (2013) 232–247.
• Ariel L. Lombardi. The dicrete compactness property for edge elements of any order on polyhedral domains. ESAIM Math. Model. Numer. Anal. 47 (2013) 169–181.
• Leandro M. Del Pezzo, Ariel L. Lombardi, Sandra R. Martínez. IP-DGFEM method for the p(x)- Laplacian. SIAM J. Numer. Anal. 50#5 (2012) 2497–2521.
• Ariel L. Lombardi, Paola Pietra. Exponentially Fitted Discontinuous Galerkin Schemes for Singularly Perturbed Problems. Numer. Meth. Partial Diff. Eq. 28 #6 (2012) 1747–1777.
• Ricardo G. Durán, Ariel L. Lombardi, Mariana I. Prieto. Superconvergence for finite element approximations of a convection-diffusion equation using graded meshes. IMA J. Numer. Anal. 32 #2 (2012) 511–533.
• Ariel L. Lombardi. Interpolation error estimates for edge elements on anisotropic meshes. IMA J. Numer. Anal. 31 #4 (2011) 1683–1712.
• Gabriel Acosta, Thomas Apel, Ricardo G. Durán, Ariel L. Lombardi. Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra. Math. Comp. 80 #273 (2011) 141–163.
• Thomas Apel, Gabriel Acosta, Ricardo G. Durán, Ariel L. Lombardi. Anisotropic error estimates for an interpolant defined via moments. Computing 82 (2008) 1–9.
• Ricardo G. Durán, Ariel L. Lombardi. Error estimates for the Raviart-Thomas interpolation under the maximum angle condition. SIAM J. Numer. Anal. 46 (2008) 1442–1453.
• G. Acosta, M. G. Armentano, R. G. Durán and A. L. Lombardi. Finite element approximations in a non-Lipschitz domain. SIAM J. Numer. Anal. 45 #1 (2007) 277–295.
• Ricardo G. Durán, Ariel L. Lombardi. Finite element approximation of convection diffusion problems using graded meshes. Appl. Numer. Math. 56 (2006) 1314–1325.
• Gabriel Acosta, Ricardo G. Durán, Ariel L. Lombardi. Weighted Poincaré and Korn Inequalities for Hölder α Domains. Math. Meth. Appl. Sci. (MMAS) 29 #4 (2006) 387–400.
• Gabriel Acosta, María G. Armentano, Ricardo G. Durán. Ariel L. Lombardi. Nonhomogeneous Neumann problem for the Poisson equation in cuspidal domains. J. Math. Anal. Appl. 310 #2 (2005) 397–411.
• Ricardo G. Durán, Ariel L. Lombardi. Error Estimates on Anisotropic Q₁ Elements for Functions in Weighted Sobolev Spaces. Math. Comp. 74 (2005) 1679–1706.
• Ariel L. Lombardi, Domingo A. Tarzia. Similarity Solutions for thawing processes with a heat flux condition at the fixed boundary. Meccanica 36 (2001) 251–264.
• Lucio R. Berrone, Ariel L. Lombardi. A note on equivalence of means. Publicationes Mathematicae Debrecen 58 #1–2 (2001) 49–56.
• Mabel M. Tidball, Ariel Lombardi, Odile Pourtallier, Eitan Altman. Continuity of optimal values and solutions for control of Markov chains with constraints. SIAM J. Control and Optim. 38 #4 (2000) 1204–1222.