A Hierarchical Domain Decomposition Preconditioner for h-P Finite Element Approximation on Locally Refined Meshes. - Mark Ainsworth (SIAM J. Sci. Comput., 1996)

A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains. - Mark Ainsworth (Numerische Mathematik, 1998)

The approximation theory for the p-version finite element method and application to non-linear elliptic PDEs. - Mark Ainsworth; David Kay (Numerische Mathematik, 1999)

An additive Schwarz preconditioner for p-version boundary element approximation of the hypersingular operator in three dimensions. - Mark Ainsworth; Benqi Guo (Numerische Mathematik, 2000)

The Stability of Mixed hp-Finite Element Methods for Stokes Flow on High Aspect Ratio Elements. - Mark Ainsworth; Patrick Coggins (SIAM J. Numer. Anal., 2000)

Construction and Analysis of Optimal Hierarchic Models of Boundary Value Problems on Thin Circular and Spherical Geometries. - Mark Ainsworth; Mark Arnold (SIAM J. Sci. Comput., 2000)

A Posteriori Error Estimators and Adaptivity for Finite Element Approximation of the Non-Homogeneous Dirichlet Problem. - Mark Ainsworth; Donald W. Kelly (Adv. Comput. Math., 2001)

Fundamental Systems of Numerical Schemes for Linear Convection-Diffusion Equations and their Relationship to Accuracy. - Mark Ainsworth; Willy Dörfler (Computing, 2001)

hp-Approximation Theory for BDFM and RT Finite Elements on Quadrilaterals. - Mark Ainsworth; Katia Pinchedez (SIAM J. Numer. Anal., 2002)

Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes. - Mark Ainsworth; William McLean (Numerische Mathematik, 2003)

Conditioning of Hierarchic p-Version Nédélec Elements on Meshes of Curvilinear Quadrilaterals and Hexahedra. - Mark Ainsworth; Joe Coyle (SIAM J. Numer. Anal., 2003)

Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number. - Mark Ainsworth (SIAM J. Numer. Anal., 2004)

Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow. - Willy Dörfler; Mark Ainsworth (Math. Comput., 2005)

Robust A Posteriori Error Estimation for Nonconforming Finite Element Approximation. - Mark Ainsworth (SIAM J. Numer. Anal., 2005)

Dispersive and Dissipative Properties of Discontinuous Galerkin Finite Element Methods for the Second-Order Wave Equation. - Mark Ainsworth; Peter Monk 001; Wagner Muniz (J. Sci. Comput., 2006)

A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation. - Mark Ainsworth (SIAM J. Numer. Anal., 2007)

A Posteriori Error Estimation for Lowest Order Raviart-Thomas Mixed Finite Elements. - Mark Ainsworth (SIAM J. Sci. Comput., 2007)

Robust a posteriori error estimation for the nonconforming Fortin-Soulie finite element approximation. - Mark Ainsworth; Richard Rankin (Math. Comput., 2008)

Fully Computable Bounds for the Error in Nonconforming Finite Element Approximations of Arbitrary Order on Triangular Elements. - Mark Ainsworth; Richard Rankin (SIAM J. Numer. Anal., 2008)

Dispersive and Dissipative Behavior of the Spectral Element Method. - Mark Ainsworth; Hafiz Abdul Wajid (SIAM J. Numer. Anal., 2009)

A framework for obtaining guaranteed error bounds for finite element approximations. - Mark Ainsworth (J. Comput. Appl. Math., 2010)

Fully Computable Error Bounds for Discontinuous Galerkin Finite Element Approximations on Meshes with an Arbitrary Number of Levels of Hanging Nodes. - Mark Ainsworth; Richard Rankin (SIAM J. Numer. Anal., 2010)

Optimally Blended Spectral-Finite Element Scheme for Wave Propagation and NonStandard Reduced Integration. - Mark Ainsworth; Hafiz Abdul Wajid (SIAM J. Numer. Anal., 2010)

Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems. - Mark Ainsworth; Tomás Vejchodský (Numerische Mathematik, 2011)

Bernstein-Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures. - Mark Ainsworth; Gaelle Andriamaro; Oleg Davydov (SIAM J. Sci. Comput., 2011)

Non-uniform order mixed FEM approximation: Implementation, post-processing, computable error bound and adaptivity. - Mark Ainsworth; Xinhui Ma (J. Comput. Phys., 2012)

On the Adaptive Selection of the Parameter in Stabilized Finite Element Approximations. - Mark Ainsworth; Alejandro Allendes; Gabriel R. Barrenechea; Richard Rankin (SIAM J. Numer. Anal., 2013)

Dispersive behaviour of high order finite element schemes for the one-way wave equation. - Mark Ainsworth (J. Comput. Phys., 2014)

Pyramid Algorithms for Bernstein-Bézier Finite Elements of High, Nonuniform Order in Any Dimension. - Mark Ainsworth (SIAM J. Sci. Comput., 2014)

Multigrid at Scale? - Mark Ainsworth; Christian Glusa (ENUMATH, 2015)

Stabilization of High Aspect Ratio Mixed Finite Elements for Incompressible Flow. - Mark Ainsworth; Gabriel R. Barrenechea; Andreas Wachtel (SIAM J. Numer. Anal., 2015)

Tempered Fractional Sturm-Liouville EigenProblems. - Mohsen Zayernouri; Mark Ainsworth; George E. Karniadakis (SIAM J. Sci. Comput., 2015)

Discrete extension operators for mixed finite element spaces on locally refined meshes. - Mark Ainsworth; Johnny Guzmán; Francisco-Javier Sayas (Math. Comput., 2016)

Computing the Bézier Control Points of the Lagrangian Interpolant in Arbitrary Dimension. - Mark Ainsworth; Manuel A. Sánchez (SIAM J. Sci. Comput., 2016)

Canopus: A Paradigm Shift Towards Elastic Extreme-Scale Data Analytics on HPC Storage. - Tao Lu; Eric Suchyta; David Pugmire; Jong Choi 001; Scott Klasky; Qing Liu 002; Norbert Podhorszki; Mark Ainsworth; Matthew Wolf (CLUSTER, 2017)

Computing Just What You Need: Online Data Analysis and Reduction at Extreme Scales. - Ian T. Foster; Mark Ainsworth; Bryce Allen; Julie Bessac; Franck Cappello; Jong Youl Choi; Emil M. Constantinescu; Philip E. Davis; Sheng Di; Zichao Wendy Di; Hanqi Guo 001; Scott Klasky; et al. (Euro-Par, 2017)

Canopus: Enabling Extreme-Scale Data Analytics on Big HPC Storage via Progressive Refactoring. - Tao Lu; Eric Suchyta; Jong Youl Choi; Norbert Podhorszki; Scott Klasky; Qing Liu 002; David Pugmire; Matthew Wolf; Mark Ainsworth (HotStorage, 2017)

Exacution: Enhancing Scientific Data Management for Exascale. - Scott Klasky; Eric Suchyta; Mark Ainsworth; Qing Liu 002; Ben Whitney; Matthew Wolf; Jong Youl Choi; Ian T. Foster; Mark Kim; Jeremy Logan; Kshitij Mehta; Todd S. Munson; et al. (ICDCS, 2017)

Analysis and Approximation of a Fractional Cahn-Hilliard Equation. - Mark Ainsworth; Zhiping Mao (SIAM J. Numer. Anal., 2017)

Is the Multigrid Method Fault Tolerant? The Two-Grid Case. - Mark Ainsworth; Christian Glusa (SIAM J. Sci. Comput., 2017)

Is the Multigrid Method Fault Tolerant? The Multilevel Case. - Mark Ainsworth; Christian Glusa (SIAM J. Sci. Comput., 2017)

Compression Using Lossless Decimation: Analysis and Application. - Mark Ainsworth; Scott Klasky; Ben Whitney (SIAM J. Sci. Comput., 2017)

Coupling Exascale Multiphysics Applications: Methods and Lessons Learned. - Jong Youl Choi; Choong-Seock Chang; Julien Dominski; Scott Klasky; Gabriele Merlo; Eric Suchyta; Mark Ainsworth; Bryce Allen; Franck Cappello; Michael Churchill; Philip E. Davis; Sheng Di; et al. (eScience, 2018)

A View from ORNL: Scientific Data Research Opportunities in the Big Data Age. - Scott Klasky; Matthew Wolf; Mark Ainsworth; Chuck Atkins; Jong Choi 001; Greg Eisenhauer; Berk Geveci; William F. Godoy; Mark Kim; James Kress; Tahsin M. Kurç; Qing Liu 002; et al. (ICDCS, 2018)

Multilevel techniques for compression and reduction of scientific data - the univariate case. - Mark Ainsworth; Ozan Tugluk; Ben Whitney; Scott Klasky (Comput. Vis. Sci., 2018)

Fully Computable a Posteriori Error Bounds for Hybridizable Discontinuous Galerkin Finite Element Approximations. - Mark Ainsworth; Guosheng Fu (J. Sci. Comput., 2018)

Hybrid Finite Element-Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver. - Mark Ainsworth; Christian Glusa (SIAM J. Sci. Comput., 2018)

Dispersive Behavior of an Energy-Conserving Discontinuous Galerkin Method for the One-Way Wave Equation. - Mark Ainsworth; Guosheng Fu (J. Sci. Comput., 2019)

Preconditioning the Mass Matrix for High Order Finite Element Approximation on Triangles. - Mark Ainsworth; Shuai Jiang (SIAM J. Numer. Anal., 2019)

Multilevel Techniques for Compression and Reduction of Scientific Data - The Multivariate Case. - Mark Ainsworth; Ozan Tugluk; Ben Whitney; Scott Klasky (SIAM J. Sci. Comput., 2019)

Multilevel Techniques for Compression and Reduction of Scientific Data-Quantitative Control of Accuracy in Derived Quantities. - Mark Ainsworth; Ozan Tugluk; Ben Whitney; Scott Klasky (SIAM J. Sci. Comput., 2019)

Extending the Publish/Subscribe Abstraction for High-Performance I/O and Data Management at Extreme Scale. - Jeremy Logan; Mark Ainsworth; Chuck Atkins; Jieyang Chen; Jong Choi 001; Junmin Gu; James Kress; Greg Eisenhauer; Berk Geveci; William F. Godoy; Mark Kim; Tahsin M. Kurç; et al. (IEEE Data Eng. Bull., 2020)

What is the fractional Laplacian? A comparative review with new results. - Anna Lischke; Guofei Pang; Mamikon A. Gulian; Fangying Song; Christian Glusa; Xiaoning Zheng; Zhiping Mao; Wei Cai 003; Mark M. Meerschaert; Mark Ainsworth; George Em Karniadakis (J. Comput. Phys., 2020)

H2-Stable Polynomial Liftings on Triangles. - Mark Ainsworth; Charles Parker 001 (SIAM J. Numer. Anal., 2020)

Multilevel Techniques for Compression and Reduction of Scientific Data - The Unstructured Case. - Mark Ainsworth; Ozan Tugluk; Ben Whitney; Scott Klasky (SIAM J. Sci. Comput., 2020)

Maintaining Trust in Reduction: Preserving the Accuracy of Quantities of Interest for Lossy Compression. - Qian Gong; Xin Liang 001; Ben Whitney; Jong Youl Choi; Jieyang Chen; Lipeng Wan 001; Stéphane Ethier; Seung-Hoe Ku; Randy Michael Churchill; Choong-Seock Chang; Mark Ainsworth; Ozan Tugluk; et al. (SMC, 2021)

Online data analysis and reduction: An important Co-design motif for extreme-scale computers. - Ian T. Foster; Mark Ainsworth; Julie Bessac; Franck Cappello; Jong Choi 001; Sheng Di; Zichao Wendy Di; Ali Murat Gok; Hanqi Guo 001; Kevin A. Huck; Christopher Kelly; Scott Klasky; et al. (Int. J. High Perform. Comput. Appl., 2021)

Preconditioning high order H2 conforming finite elements on triangles. - Mark Ainsworth; Charles Parker 001 (Numerische Mathematik, 2021)

Mass Conserving Mixed hp-FEM Approximations to Stokes Flow. Part I: Uniform Stability. - Mark Ainsworth; Charles Parker 001 (SIAM J. Numer. Anal., 2021)

Mass Conserving Mixed hp-FEM Approximations to Stokes Flow. Part II: Optimal Convergence. - Mark Ainsworth; Charles Parker 001 (SIAM J. Numer. Anal., 2021)

Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control. - Mark Ainsworth; Justin Dong (SIAM J. Sci. Comput., 2021)

Preconditioning the Mass Matrix for High Order Finite Element Approximation on Tetrahedra. - Mark Ainsworth; Shuai Jiang (SIAM J. Sci. Comput., 2021)

Plateau Phenomenon in Gradient Descent Training of RELU Networks: Explanation, Quantification, and Avoidance. - Mark Ainsworth; Yeonjong Shin (SIAM J. Sci. Comput., 2021)

A Systematic Approach to Constructing Preconditioners for the $hp$-Version Mass Matrix on Unstructured and Hybrid Finite Element Meshes. - Mark Ainsworth; Shuai Jiang (SIAM J. Sci. Comput., 2022)

A Mass Conserving Mixed $hp$-FEM Scheme for Stokes Flow. Part III: Implementation and Preconditioning. - Mark Ainsworth; Charles Parker 001 (SIAM J. Numer. Anal., 2022)

Active Neuron Least Squares: A Training Method for Multivariate Rectified Neural Networks. - Mark Ainsworth; Yeonjong Shin (SIAM J. Sci. Comput., 2022)

Computing H2-conforming finite element approximations without having to implement C1-elements. - Mark Ainsworth; Charles Parker 001 (CoRR, 2023)

Uniform preconditioners for high order finite element approximations of planar linear elasticity. - Mark Ainsworth; Charles Parker 001 (Math. Comput., 2023)

Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow. - Mark Ainsworth; Charles Parker 001 (SIAM J. Sci. Comput., 2023)

Two and three dimensional H2-conforming finite element approximations without C1-elements. - Mark Ainsworth; Charles Parker 001 (CoRR, 2024)

Uniform Substructuring Preconditioners for High Order FEM on Triangles and the Influence of Nodal Basis Functions. - Mark Ainsworth; Shuai Jiang (SIAM J. Numer. Anal., 2024)

Computing ( boldsymbol{H}^{ boldsymbol{2}} )-Conforming Finite Element Approximations Without Having to Implement ( boldsymbol{C}^{ boldsymbol{1}} )-Elements. - Mark Ainsworth; Charles Parker 001 (SIAM J. Sci. Comput., 2024)

Extended Galerkin Neural Network Approximation of Singular Variational Problems with Error Control. - Mark Ainsworth; Justin Dong (SIAM J. Sci. Comput., 2025)

Do locking-free finite element schemes lock for holey Reissner-Mindlin plates with mixed boundary conditions? - Mark Ainsworth; Charles Parker 001 (CoRR, 2025)