Analysis of a Stabilized Finite Element Approximation of the Transient Convection-Diffusion Equation Using an ALE Framework. - Santiago Badia; Ramon Codina (SIAM J. Numer. Anal., 2006)

Bridging Methods for Coupling Atomistic and Continuum Models. - Santiago Badia; Pavel B. Bochev; Max D. Gunzburger; Richard B. Lehoucq; Michael L. Parks (LSSC, 2007)

Convergence analysis of the FEM approximation of the first order projection method for incompressible flows with and without the inf-sup condition. - Santiago Badia; Ramon Codina (Numerische Mathematik, 2007)

Fluid-structure partitioned procedures based on Robin transmission conditions. - Santiago Badia; Fabio Nobile; Christian Vergara (J. Comput. Phys., 2008)

On Atomistic-to-Continuum Coupling by Blending. - Santiago Badia; Michael L. Parks; Pavel B. Bochev; Max D. Gunzburger; Richard B. Lehoucq (Multiscale Model. Simul., 2008)

Splitting Methods Based on Algebraic Factorization for Fluid-Structure Interaction. - Santiago Badia; Annalisa Quaini; Alfio Quarteroni (SIAM J. Sci. Comput., 2008)

On a multiscale approach to the transient Stokes problem: Dynamic subscales and anisotropic space-time discretization. - Santiago Badia; Ramon Codina (Appl. Math. Comput., 2009)

Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction. - Santiago Badia; Annalisa Quaini; Alfio Quarteroni (J. Comput. Phys., 2009)

Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems. - Santiago Badia; Ramon Codina (SIAM J. Numer. Anal., 2009)

Long-Term Stability Estimates and Existence of a Global Attractor in a Finite Element Approximation of the Navier-Stokes Equations with Numerical Subgrid Scale Modeling. - Santiago Badia; Ramon Codina; Juan Vicente Gutiérrez-Santacreu (SIAM J. Numer. Anal., 2010)

A combined nodal continuous-discontinuous finite element formulation for the Maxwell problem. - Santiago Badia; Ramon Codina (Appl. Math. Comput., 2011)

Finite element approximation of nematic liquid crystal flows using a saddle-point structure. - Santiago Badia; Francisco Guillén-González; Juan Vicente Gutiérrez-Santacreu (J. Comput. Phys., 2011)

Approximation of the inductionless MHD problem using a stabilized finite element method. - Ramon Planas; Santiago Badia; Ramon Codina (J. Comput. Phys., 2011)

A Nodal-based Finite Element Approximation of the Maxwell Problem Suitable for Singular Solutions. - Santiago Badia; Ramon Codina (SIAM J. Numer. Anal., 2012)

On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics. - Santiago Badia; Ramon Codina; Ramon Planas (J. Comput. Phys., 2013)

Adaptive Finite Element Simulation of Incompressible Flows by Hybrid Continuous-Discontinuous Galerkin Formulations. - Santiago Badia; Joan Baiges (SIAM J. Sci. Comput., 2013)

Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem. - Santiago Badia; Alberto F. Martín; Ramon Planas (J. Comput. Phys., 2014)

Stability, Convergence, and Accuracy of Stabilized Finite Element Methods for the Wave Equation in Mixed Form. - Santiago Badia; Ramon Codina; Hector Espinoza (SIAM J. Numer. Anal., 2014)

On Monotonicity-Preserving Stabilized Finite Element Approximations of Transport Problems. - Santiago Badia; Alba Hierro (SIAM J. Sci. Comput., 2014)

A Highly Scalable Parallel Implementation of Balancing Domain Decomposition by Constraints. - Santiago Badia; Alberto F. Martín; Javier Principe (SIAM J. Sci. Comput., 2014)

On the scalability of inexact balancing domain decomposition by constraints with overlapped coarse/fine corrections. - Santiago Badia; Alberto F. Martín; Javier Principe (Parallel Comput., 2015)

Monotonicity-preserving finite element schemes based on differentiable nonlinear stabilization. - Santiago Badia; Jesús Bonilla (CoRR, 2016)

Differentiable monotonicity-preserving schemes for discontinuous Galerkin methods on arbitrary meshes. - Santiago Badia; Jesús Bonilla; Alba Hierro (CoRR, 2016)

Balancing Domain Decomposition by Constraints and Perturbation. - Santiago Badia; Hieu Nguyen 003 (SIAM J. Numer. Anal., 2016)

Multilevel Balancing Domain Decomposition at Extreme Scales. - Santiago Badia; Alberto F. Martín; Javier Principe (SIAM J. Sci. Comput., 2016)

FEMPAR: An object-oriented parallel finite element framework. - Santiago Badia; Alberto F. Martín; Javier Principe (CoRR, 2017)

The aggregated unfitted finite element method for elliptic problems. - Santiago Badia; Francesc Verdugo; Alberto F. Martín (CoRR, 2017)

Convergence to Suitable Weak Solutions for a Finite Element Approximation of the Navier-Stokes Equations with Numerical Subgrid Scale Modeling. - Santiago Badia; Juan Vicente Gutiérrez-Santacreu (J. Sci. Comput., 2017)

Space-Time Balancing Domain Decomposition. - Santiago Badia; Marc Olm (SIAM J. Sci. Comput., 2017)

A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing. - Eric Neiva; Santiago Badia; Alberto F. Martín; Michele Chiumenti (CoRR, 2018)

Numerical modelling of heat transfer and experimental validation in Powder-Bed Fusion with the Virtual Domain Approximation. - Eric Neiva; Michele Chiumenti; Miguel Cervera; Emilio Salsi; Gabriele Piscopo; Santiago Badia; Alberto F. Martín; Zhuoer Chen; Caroline Lee; Christopher Davies 002 (CoRR, 2018)

Maximum-principle preserving space-time isogeometric analysis. - Jesús Bonilla; Santiago Badia (CoRR, 2018)

Nonlinear parallel-in-time Schur complement solvers for ordinary differential equations. - Santiago Badia; Marc Olm (J. Comput. Appl. Math., 2018)

Robust and scalable domain decomposition solvers for unfitted finite element methods. - Santiago Badia; Francesc Verdugo (J. Comput. Appl. Math., 2018)

Editorial: Algorithmic Aspects of High-Performance Computing for Mechanics and Physics. - Victor M. Calo; Santiago Badia; Javier Principe (J. Comput. Appl. Math., 2018)

Mixed Aggregated Finite Element Methods for the Unfitted Discretization of the Stokes Problem. - Santiago Badia; Alberto F. Martín; Francesc Verdugo (SIAM J. Sci. Comput., 2018)

On a general implementation of h- and p-adaptive curl-conforming finite elements. - Marc Olm; Santiago Badia; Alberto F. Martín (Adv. Eng. Softw., 2019)

Balancing domain decomposition by constraints associated with subobjects. - Santiago Badia; Alberto F. Martín; Hieu Nguyen 003 (Appl. Math. Lett., 2019)

Scalable solvers for complex electromagnetics problems. - Santiago Badia; Alberto F. Martín; Marc Olm (CoRR, 2019)

Distributed-memory parallelization of the aggregated unfitted finite element method. - Francesc Verdugo; Alberto F. Martín; Santiago Badia (CoRR, 2019)

A user-guide to Gridap - grid-based approximation of partial differential equations in Julia. - Francesc Verdugo; Santiago Badia (CoRR, 2019)

On differentiable local bounds preserving stabilization for Euler equations. - Santiago Badia; Jesús Bonilla; Sibusiso Mabuza; John N. Shadid (CoRR, 2019)

Embedded multilevel Monte Carlo for uncertainty quantification in random domains. - Santiago Badia; Jerrad Hampton; Javier Principe (CoRR, 2019)

Simulation of High Temperature Superconductors and experimental validation. - Marc Olm; Santiago Badia; Alberto F. Martín (Comput. Phys. Commun., 2019)

Physics-Based Balancing Domain Decomposition by Constraints for Multi-Material Problems. - Santiago Badia; Alberto F. Martín; Hieu Nguyen 003 (J. Sci. Comput., 2019)

Robust and scalable h-adaptive aggregated unfitted finite elements for interface elliptic problems. - Eric Neiva; Santiago Badia (CoRR, 2020)

A robust and scalable unfitted adaptive finite element framework for nonlinear solid mechanics. - Santiago Badia; Manuel Caicedo; Alberto F. Martín; Javier Principe (CoRR, 2020)

A tutorial-driven introduction to the parallel finite element library FEMPAR v1.0.0. - Santiago Badia; Alberto F. Martín (Comput. Phys. Commun., 2020)

Monotonicity-preserving finite element schemes with adaptive mesh refinement for hyperbolic problems. - Jesús Bonilla; Santiago Badia (J. Comput. Phys., 2020)

Gridap: An extensible Finite Element toolbox in Julia. - Santiago Badia; Francesc Verdugo (J. Open Source Softw., 2020)

A Generic Finite Element Framework on Parallel Tree-Based Adaptive Meshes. - Santiago Badia; Alberto F. Martín; Eric Neiva; Francesc Verdugo (SIAM J. Sci. Comput., 2020)

Linking ghost penalty and aggregated unfitted methods. - Santiago Badia; Eric Neiva; Francesc Verdugo (CoRR, 2021)

The Aggregated Unfitted Finite Element Method on Parallel Tree-Based Adaptive Meshes. - Santiago Badia; Alberto F. Martín; Eric Neiva; Francesc Verdugo (SIAM J. Sci. Comput., 2021)

Robust high-order unfitted finite elements by interpolation-based discrete extension. - Santiago Badia; Eric Neiva; Francesc Verdugo (Comput. Math. Appl., 2022)

A comparison of variational upwinding schemes for geophysical fluids, and their application to potential enstrophy conserving discretisations in space and time. - David Lee; Alberto F. Martín; Christopher Bladwell; Santiago Badia (CoRR, 2022)

Space-time aggregated finite element methods for time-dependent problems on moving domains. - Santiago Badia; Hridya Dilip; Francesc Verdugo (CoRR, 2022)

Bound-preserving finite element approximations of the Keller-Segel equations. - Santiago Badia; Jesús Bonilla; Juan Vicente Gutiérrez-Santacreu (CoRR, 2022)

Stability and conditioning of immersed finite element methods: analysis and remedies. - Frits de Prenter; Clemens Verhoosel; Harald van Brummelen; Mats G. Larson; Santiago Badia (CoRR, 2022)

The software design of Gridap: A Finite Element package based on the Julia JIT compiler. - Francesc Verdugo; Santiago Badia (Comput. Phys. Commun., 2022)

Geometrical discretisations for unfitted finite elements on explicit boundary representations. - Santiago Badia; Pere A. Martorell; Francesc Verdugo (J. Comput. Phys., 2022)

GridapDistributed: a massively parallel finite element toolbox in Julia. - Santiago Badia; Alberto F. Martín; Francesc Verdugo (J. Open Source Softw., 2022)

Conditioning of a Hybrid High-Order Scheme on Meshes with Small Faces. - Santiago Badia; Jérôme Droniou; Liam Yemm (J. Sci. Comput., 2022)

Neural Level Set Topology Optimization Using Unfitted Finite Elements. - Connor N. Mallon; Aaron W. Thornton; Matthew R. Hill; Santiago Badia (CoRR, 2023)

Finite element interpolated neural networks for solving forward and inverse problems. - Santiago Badia; Wei Li; Alberto F. Martín (CoRR, 2023)

Space-time unfitted finite element methods for time-dependent problems on moving domains. - Santiago Badia; Hridya Dilip; Francesc Verdugo (Comput. Math. Appl., 2023)

A massively parallel implementation of multilevel Monte Carlo for finite element models. - Santiago Badia; Jerrad Hampton; Javier Principe (Math. Comput. Simul., 2023)

Efficient and reliable divergence-conforming methods for an elasticity-poroelasticity interface problem. - Santiago Badia; Martin Hornkjøl; Arbaz Khan; Kent-André Mardal; Alberto F. Martín; Ricardo Ruiz-Baier (Comput. Math. Appl., 2024)

A comparison of variational upwinding schemes for geophysical fluids, and their application to potential enstrophy conserving discretisations. - David Lee; Alberto F. Martín; Christopher Bladwell; Santiago Badia (Comput. Math. Appl., 2024)

Adaptive quadratures for nonlinear approximation of low-dimensional PDEs using smooth neural networks. - Alexandre Magueresse; Santiago Badia (Comput. Math. Appl., 2024)

Space-time unfitted finite elements on moving explicit geometry representations. - Santiago Badia; Pere A. Martorell; Francesc Verdugo (CoRR, 2024)

Adaptive Finite Element Interpolated Neural Networks. - Santiago Badia; Wei Li; Alberto F. Martín (CoRR, 2024)

GridapTopOpt.jl: A scalable Julia toolbox for level set-based topology optimisation. - Zachary J. Wegert; Jordi Manyer; Connor N. Mallon; Santiago Badia; Vivien J. Challis (CoRR, 2024)

A discrete trace theory for non-conforming polytopal hybrid discretisation methods. - Santiago Badia; Jérôme Droniou; Jai Tushar (CoRR, 2024)

Compatible finite element interpolated neural networks. - Santiago Badia; Wei Li; Alberto F. Martín (CoRR, 2024)

A tensor-train reduced basis solver for parameterized partial differential equations. - Nicholas Mueller; Yiran Zhao; Santiago Badia; Tiangang Cui (CoRR, 2024)

Model order reduction with novel discrete empirical interpolation methods in space-time. - Nicholas Mueller; Santiago Badia (J. Comput. Appl. Math., 2024)

High order unfitted finite element discretizations for explicit boundary representations. - Pere A. Martorell; Santiago Badia (J. Comput. Phys., 2024)

GridapSolvers.jl: Scalable multiphysics finite element solvers in Julia. - Jordi Manyer; Alberto F. Martín; Santiago Badia (J. Open Source Softw., 2024)

STLCutters.jl: A scalable geometrical framework library for unfitted finite element discretisations. - Pere A. Martorell; Santiago Badia (Comput. Phys. Commun., 2025)

Energy and entropy conserving compatible finite elements with upwinding for the thermal shallow water equations. - Tamara A. Tambyah; David Lee; Santiago Badia (J. Comput. Phys., 2025)

Unfitted finite element interpolated neural networks. - Wei Li; Alberto F. Martín; Santiago Badia (CoRR, 2025)

A framework for efficient reduced order modelling in the Julia programming language. - Nicholas Mueller; Santiago Badia (CoRR, 2025)

Level-set topology optimisation with unfitted finite elements and automatic shape differentiation. - Zachary J. Wegert; Jordi Manyer; Connor N. Mallon; Santiago Badia; Vivien J. Challis (CoRR, 2025)

Non-augmented velocity-vorticity-pressure formulation for the Navier-Stokes-Brinkman-Forchheimer problem. - Santiago Badia; Carsten Carstensen; Alberto F. Martín; Ricardo Ruiz-Baier; Segundo Villa-Fuentes (CoRR, 2025)

Analysis of BDDC preconditioners for non-conforming polytopal hybrid discretisation methods. - Santiago Badia; Jérôme Droniou; Jordi Manyer; Jai Tushar (CoRR, 2025)

Reduced basis solvers for unfitted methods on parameterized domains. - Nicholas Mueller; Santiago Badia; Yiran Zhao (CoRR, 2025)

A tensor-train reduced basis solver for parameterized partial differential equations on Cartesian grids. - Nicholas Mueller; Yiran Zhao; Santiago Badia; Tiangang Cui (J. Comput. Appl. Math., 2026)