Ariel L. Lombardi

Mathematics Professor and Researcher

• Full 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

• A. Arós, A.L. Lombardi, L. Venturato Mathematical and numerical analysis of Koiter elliptic shells in normal compliance contact. Mathematics and Mechanics of Solids. 2025;0(0)
• M. Barrios, A.L. Lombardi, C. Penessi A finite element discretization of fractional problems using graded meshes. Journal of Computational and Applied Mathematics 473 (2026) 116832
• R. Bustinza , M. Cicuttin, A.L. Lombardi A hybrid high-order method for the mixed Steklov eigenvalue problem. Numerische Mathematik 157 (2025) 447-475, DOI https://doi.org/10.1007/s00211-025-01463-w
• 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 25, no. 2 (2025) 263-285. doi: 10.1515/cmam-2023-0219.
• 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.
• A.L. Lombardi, P. Pietra, M.I. Prieto. A posteriori error estimator for exponentially fitted Discontinuous Galerkin approximation of advection dominated problems. Calcolo 53 (2016) 83-103. doi: 10.1007/s10092-015-0138-z.
• 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.

Finite Elements and Related Numerical Methods

We develop and analyze finite element methods and related numerical schemes that are robust for singularly perturbed partial differential equations and systems, for elliptic problems with vertex and edge singularities, and on anisotropic meshes, including VEM and HHO approximations.

Research group at the Departamento de Matemática, ECEN - FCEIA, Universidad Nacional de Rosario.

Members