Mark Ainsworth

According to our database1, Mark Ainsworth authored at least 73 papers between 1996 and 2024.

Collaborative distances:
  • Dijkstra number2 of four.
  • Erdős number3 of four.

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Bibliography

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

Uniform Substructuring Preconditioners for High Order FEM on Triangles and the Influence of Nodal Basis Functions.
SIAM J. Numer. Anal., 2024

Two and three dimensional H<sup>2</sup>-conforming finite element approximations without C<sup>1</sup>-elements.
CoRR, 2024

Extended Galerkin neural network approximation of singular variational problems with error control.
CoRR, 2024

2023
Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow.
SIAM J. Sci. Comput., June, 2023

Uniform preconditioners for high order finite element approximations of planar linear elasticity.
Math. Comput., 2023

Computing H<sup>2</sup>-conforming finite element approximations without having to implement C<sup>1</sup>-elements.
CoRR, 2023

2022
Active Neuron Least Squares: A Training Method for Multivariate Rectified Neural Networks.
SIAM J. Sci. Comput., August, 2022

A Mass Conserving Mixed $hp$-FEM Scheme for Stokes Flow. Part III: Implementation and Preconditioning.
SIAM J. Numer. Anal., June, 2022

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

2021
Plateau Phenomenon in Gradient Descent Training of RELU Networks: Explanation, Quantification, and Avoidance.
SIAM J. Sci. Comput., 2021

Preconditioning the Mass Matrix for High Order Finite Element Approximation on Tetrahedra.
SIAM J. Sci. Comput., 2021

Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control.
SIAM J. Sci. Comput., 2021

Mass Conserving Mixed hp-FEM Approximations to Stokes Flow. Part II: Optimal Convergence.
SIAM J. Numer. Anal., 2021

Mass Conserving Mixed hp-FEM Approximations to Stokes Flow. Part I: Uniform Stability.
SIAM J. Numer. Anal., 2021

Preconditioning high order H<sup>2</sup> conforming finite elements on triangles.
Numerische Mathematik, 2021

Online data analysis and reduction: An important Co-design motif for extreme-scale computers.
Int. J. High Perform. Comput. Appl., 2021

Maintaining Trust in Reduction: Preserving the Accuracy of Quantities of Interest for Lossy Compression.
Proceedings of the Driving Scientific and Engineering Discoveries Through the Integration of Experiment, Big Data, and Modeling and Simulation, 2021

2020
Multilevel Techniques for Compression and Reduction of Scientific Data - The Unstructured Case.
SIAM J. Sci. Comput., 2020

H<sup>2</sup>-Stable Polynomial Liftings on Triangles.
SIAM J. Numer. Anal., 2020

What is the fractional Laplacian? A comparative review with new results.
J. Comput. Phys., 2020

Extending the Publish/Subscribe Abstraction for High-Performance I/O and Data Management at Extreme Scale.
IEEE Data Eng. Bull., 2020

2019
Multilevel Techniques for Compression and Reduction of Scientific Data-Quantitative Control of Accuracy in Derived Quantities.
SIAM J. Sci. Comput., 2019

Multilevel Techniques for Compression and Reduction of Scientific Data - The Multivariate Case.
SIAM J. Sci. Comput., 2019

Preconditioning the Mass Matrix for High Order Finite Element Approximation on Triangles.
SIAM J. Numer. Anal., 2019

Dispersive Behavior of an Energy-Conserving Discontinuous Galerkin Method for the One-Way Wave Equation.
J. Sci. Comput., 2019

2018
Hybrid Finite Element-Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver.
SIAM J. Sci. Comput., 2018

Fully Computable a Posteriori Error Bounds for Hybridizable Discontinuous Galerkin Finite Element Approximations.
J. Sci. Comput., 2018

Multilevel techniques for compression and reduction of scientific data - the univariate case.
Comput. Vis. Sci., 2018

A View from ORNL: Scientific Data Research Opportunities in the Big Data Age.
Proceedings of the 38th IEEE International Conference on Distributed Computing Systems, 2018


2017
Compression Using Lossless Decimation: Analysis and Application.
SIAM J. Sci. Comput., 2017

Is the Multigrid Method Fault Tolerant? The Multilevel Case.
SIAM J. Sci. Comput., 2017

Is the Multigrid Method Fault Tolerant? The Two-Grid Case.
SIAM J. Sci. Comput., 2017

Analysis and Approximation of a Fractional Cahn-Hilliard Equation.
SIAM J. Numer. Anal., 2017

Exacution: Enhancing Scientific Data Management for Exascale.
Proceedings of the 37th IEEE International Conference on Distributed Computing Systems, 2017

Canopus: Enabling Extreme-Scale Data Analytics on Big HPC Storage via Progressive Refactoring.
Proceedings of the 9th USENIX Workshop on Hot Topics in Storage and File Systems, 2017

Computing Just What You Need: Online Data Analysis and Reduction at Extreme Scales.
Proceedings of the Euro-Par 2017: Parallel Processing - 23rd International Conference on Parallel and Distributed Computing, Santiago de Compostela, Spain, August 28, 2017

Canopus: A Paradigm Shift Towards Elastic Extreme-Scale Data Analytics on HPC Storage.
Proceedings of the 2017 IEEE International Conference on Cluster Computing, 2017

2016
Computing the Bézier Control Points of the Lagrangian Interpolant in Arbitrary Dimension.
SIAM J. Sci. Comput., 2016

Discrete extension operators for mixed finite element spaces on locally refined meshes.
Math. Comput., 2016

2015
Tempered Fractional Sturm-Liouville EigenProblems.
SIAM J. Sci. Comput., 2015

Stabilization of High Aspect Ratio Mixed Finite Elements for Incompressible Flow.
SIAM J. Numer. Anal., 2015

Multigrid at Scale?
Proceedings of the Numerical Mathematics and Advanced Applications - ENUMATH 2015, 2015

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

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

2013
On the Adaptive Selection of the Parameter in Stabilized Finite Element Approximations.
SIAM J. Numer. Anal., 2013

2012
Non-uniform order mixed FEM approximation: Implementation, post-processing, computable error bound and adaptivity.
J. Comput. Phys., 2012

2011
Bernstein-Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures.
SIAM J. Sci. Comput., 2011

Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems.
Numerische Mathematik, 2011

2010
Optimally Blended Spectral-Finite Element Scheme for Wave Propagation and NonStandard Reduced Integration.
SIAM J. Numer. Anal., 2010

Fully Computable Error Bounds for Discontinuous Galerkin Finite Element Approximations on Meshes with an Arbitrary Number of Levels of Hanging Nodes.
SIAM J. Numer. Anal., 2010

A framework for obtaining guaranteed error bounds for finite element approximations.
J. Comput. Appl. Math., 2010

2009
Dispersive and Dissipative Behavior of the Spectral Element Method.
SIAM J. Numer. Anal., 2009

2008
Fully Computable Bounds for the Error in Nonconforming Finite Element Approximations of Arbitrary Order on Triangular Elements.
SIAM J. Numer. Anal., 2008

Robust a posteriori error estimation for the nonconforming Fortin-Soulie finite element approximation.
Math. Comput., 2008

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

A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation.
SIAM J. Numer. Anal., 2007

2006
Dispersive and Dissipative Properties of Discontinuous Galerkin Finite Element Methods for the Second-Order Wave Equation.
J. Sci. Comput., 2006

2005
Robust A Posteriori Error Estimation for Nonconforming Finite Element Approximation.
SIAM J. Numer. Anal., 2005

Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow.
Math. Comput., 2005

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

2003
Conditioning of Hierarchic <i>p</i>-Version Nédélec Elements on Meshes of Curvilinear Quadrilaterals and Hexahedra.
SIAM J. Numer. Anal., 2003

Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes.
Numerische Mathematik, 2003

2002
<i>hp</i>-Approximation Theory for BDFM and RT Finite Elements on Quadrilaterals.
SIAM J. Numer. Anal., 2002

2001
Fundamental Systems of Numerical Schemes for Linear Convection-Diffusion Equations and their Relationship to Accuracy.
Computing, 2001

A Posteriori Error Estimators and Adaptivity for Finite Element Approximation of the Non-Homogeneous Dirichlet Problem.
Adv. Comput. Math., 2001

2000
Construction and Analysis of Optimal Hierarchic Models of Boundary Value Problems on Thin Circular and Spherical Geometries.
SIAM J. Sci. Comput., 2000

The Stability of Mixed <i>hp</i>-Finite Element Methods for Stokes Flow on High Aspect Ratio Elements.
SIAM J. Numer. Anal., 2000

An additive Schwarz preconditioner for p-version boundary element approximation of the hypersingular operator in three dimensions.
Numerische Mathematik, 2000

1999
The approximation theory for the <i>p</i>-version finite element method and application to non-linear elliptic PDEs.
Numerische Mathematik, 1999

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

1996
A Hierarchical Domain Decomposition Preconditioner for <i>h</i>-<i>P</i> Finite Element Approximation on Locally Refined Meshes.
SIAM J. Sci. Comput., 1996


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