Mark Ainsworth

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Dispersive and Dissipative Properties of Discontinuous Galerkin Finite Element Methods for the Second-Order Wave Equation

Mark Ainsworth, Peter Monk, W. Muniz, 2006, J. Sci. Comput..

A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains

Mark Ainsworth, M. Ainsworth, 1998, Numerische Mathematik.

Compression Using Lossless Decimation: Analysis and Application

Scott Klasky, Mark Ainsworth, Ben Whitney, 2017, SIAM J. Sci. Comput..

What Is the Fractional Laplacian

Wei Cai, Zhiping Mao, Mark Ainsworth, 2018, 1801.09767.

The graduate student's guide to numerical analysis '98 : lecture notes from the VIII EPSRC Summer School in Numerical Analysis

Mark Ainsworth, Marco Marletta, Jeremy Levesley, 1999 .

A framework for obtaining guaranteed error bounds for finite element approximations

Mark Ainsworth, M. Ainsworth, 2010, J. Comput. Appl. Math..

Robust a posteriori error estimation for the nonconforming Fortin-Soulie finite element approximation

Mark Ainsworth, Richard Rankin, M. Ainsworth, 2008, Math. Comput..

Preconditioning the Mass Matrix for High Order Finite Element Approximation on Triangles

Shuai Jiang, Mark Ainsworth, 2019, SIAM J. Numer. Anal..

Non-uniform order mixed FEM approximation: Implementation, post-processing, computable error bound and adaptivity

Mark Ainsworth, Xinhui Ma, M. Ainsworth, 2012, J. Comput. Phys..

Exacution: Enhancing Scientific Data Management for Exascale

Scott Klasky, Qing Liu, Ian T. Foster, 2017, 2017 IEEE 37th International Conference on Distributed Computing Systems (ICDCS).

Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow

Willy Dörfler, Mark Ainsworth, M. Ainsworth, 2005, Math. Comput..

Discrete extension operators for mixed finite element spaces on locally refined meshes

Mark Ainsworth, Francisco-Javier Sayas, Johnny Guzmán, 2016, Math. Comput..

Multilevel Techniques for Compression and Reduction of Scientific Data - The Multivariate Case

Scott Klasky, Mark Ainsworth, Ben Whitney, 2019, SIAM J. Sci. Comput..

Dispersive behaviour of high order finite element schemes for the one-way wave equation

Mark Ainsworth, M. Ainsworth, 2014, J. Comput. Phys..

Multilevel Techniques for Compression and Reduction of Scientific Data-Quantitative Control of Accuracy in Derived Quantities

Scott Klasky, Mark Ainsworth, Ben Whitney, 2019, SIAM J. Sci. Comput..

The approximation theory for the p-version finite element method and application to non-linear elliptic PDEs

Mark Ainsworth, David Kay, M. Ainsworth, 1999, Numerische Mathematik.

Bernstein-Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures

Mark Ainsworth, Oleg Davydov, Gaelle Andriamaro, 2011, SIAM J. Sci. Comput..

Canopus: A Paradigm Shift Towards Elastic Extreme-Scale Data Analytics on HPC Storage

Tao Lu, Scott Klasky, Qing Liu, 2017, 2017 IEEE International Conference on Cluster Computing (CLUSTER).

Topics in Computational Wave Propagation: Direct and Inverse Problems

Mark Ainsworth, M. Ainsworth, 2003 .

Stabilization of High Aspect Ratio Mixed Finite Elements for Incompressible Flow

Mark Ainsworth, Gabriel R. Barrenechea, Andreas Wachtel, 2015, SIAM J. Numer. Anal..

Hybrid Finite Element-Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver

Mark Ainsworth, Christian Glusa, 2018, SIAM J. Sci. Comput..

Dispersive Behavior of an Energy-Conserving Discontinuous Galerkin Method for the One-Way Wave Equation

Mark Ainsworth, Guosheng Fu, M. Ainsworth, 2018, J. Sci. Comput..

Optimally Blended Spectral-Finite Element Scheme for Wave Propagation and NonStandard Reduced Integration

Mark Ainsworth, Hafiz Abdul Wajid, M. Ainsworth, 2010, SIAM J. Numer. Anal..

On the Adaptive Selection of the Parameter in Stabilized Finite Element Approximations

Mark Ainsworth, Gabriel R. Barrenechea, Alejandro Allendes, 2013, SIAM J. Numer. Anal..

An additive Schwarz preconditioner for p-version boundary element approximation of the hypersingular operator in three dimensions

Mark Ainsworth, Benqi Guo, M. Ainsworth, 2000, Numerische Mathematik.

A View from ORNL: Scientific Data Research Opportunities in the Big Data Age

Scott Klasky, Qing Liu, Mark Ainsworth, 2018, 2018 IEEE 38th International Conference on Distributed Computing Systems (ICDCS).

The Stability of Mixed hp-Finite Element Methods for Stokes Flow on High Aspect Ratio Elements

Mark Ainsworth, Patrick Coggins, 2000, SIAM J. Numer. Anal..

Fully computable robust a posteriori error bounds for singularly perturbed reaction–diffusion problems

Mark Ainsworth, Tomás Vejchodský, M. Ainsworth, 2011, Numerische Mathematik.

Canopus: Enabling Extreme-Scale Data Analytics on Big HPC Storage via Progressive Refactoring

Tao Lu, Scott Klasky, Qing Liu, 2017, HotStorage.

Fully Computable a Posteriori Error Bounds for Hybridizable Discontinuous Galerkin Finite Element Approximations

Mark Ainsworth, Guosheng Fu, M. Ainsworth, 2017, Journal of Scientific Computing.

Is the Multigrid Method Fault Tolerant? The Multilevel Case

Mark Ainsworth, Christian Glusa, Christian A. Glusa, 2017, SIAM J. Sci. Comput..

Analysis and Approximation of a Fractional Cahn-Hilliard Equation

Zhiping Mao, Mark Ainsworth, M. Ainsworth, 2017, SIAM J. Numer. Anal..

A Posteriori Error Estimators and Adaptivity for Finite Element Approximation of the Non-Homogeneous Dirichlet Problem

Mark Ainsworth, Donald W. Kelly, M. Ainsworth, 2001, Adv. Comput. Math..

Computing the Bézier Control Points of the Lagrangian Interpolant in Arbitrary Dimension

Mark Ainsworth, Manuel A. Sánchez, 2016, SIAM J. Sci. Comput..

Dispersive properties of high order finite elements

Mark Ainsworth, M. Ainsworth, 2003 .

Is the Multigrid Method Fault Tolerant? The Two-Grid Case

Mark Ainsworth, Christian Glusa, Christian A. Glusa, 2016, SIAM J. Sci. Comput..

The Advanced Animal Habitat-Centrifuge (AAH-C)

Mark Ainsworth, John C. Vellinger, Mark S. Deuser, 2001 .

Multigrid at Scale?

Mark Ainsworth, Christian Glusa, 2015, ENUMATH.

Robust A Posteriori Error Estimation for Nonconforming Finite Element Approximation

Mark Ainsworth, M. Ainsworth, 2004, SIAM J. Numer. Anal..

Construction and Analysis of Optimal Hierarchic Models of Boundary Value Problems on Thin Circular and Spherical Geometries

Mark Ainsworth, Mark Arnold, 2000, SIAM J. Sci. Comput..

Coupling Exascale Multiphysics Applications: Methods and Lessons Learned

Franck Cappello, Scott Klasky, Ian T. Foster, 2018, 2018 IEEE 14th International Conference on e-Science (e-Science).

Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number

Mark Ainsworth, M. Ainsworth, 2004, SIAM J. Numer. Anal..

Fully Computable Bounds for the Error in Nonconforming Finite Element Approximations of Arbitrary Order on Triangular Elements

Mark Ainsworth, Richard Rankin, 2008, SIAM J. Numer. Anal..

A Hierarchical Domain Decomposition Preconditioner for h-P Finite Element Approximation on Locally Refined Meshes

Mark Ainsworth, 1996, SIAM J. Sci. Comput..

hp-Approximation Theory for BDFM and RT Finite Elements on Quadrilaterals

Mark Ainsworth, Katia Pinchedez, 2002, SIAM J. Numer. Anal..

A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation

Mark Ainsworth, M. Ainsworth, 2007, SIAM J. Numer. Anal..

Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes

Mark Ainsworth, William McLean, 2003, Numerische Mathematik.

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, M. Ainsworth, 2010, SIAM J. Numer. Anal..

Dispersive and Dissipative Behavior of the Spectral Element Method

Mark Ainsworth, Hafiz Abdul Wajid, M. Ainsworth, 2009, SIAM J. Numer. Anal..

Fundamental Systems of Numerical Schemes for Linear Convection–Diffusion Equations and their Relationship to Accuracy

Willy Dörfler, Mark Ainsworth, 2001, Computing.

Multilevel techniques for compression and reduction of scientific data—the univariate case

Scott Klasky, Mark Ainsworth, Ben Whitney, 2018, Comput. Vis. Sci..

Pyramid Algorithms for Bernstein-Bézier Finite Elements of High, Nonuniform Order in Any Dimension

Mark Ainsworth, M. Ainsworth, 2014, SIAM J. Sci. Comput..

A Posteriori Error Estimation for Lowest Order Raviart-Thomas Mixed Finite Elements

Mark Ainsworth, M. Ainsworth, 2007, SIAM J. Sci. Comput..

Preconditioning the Mass Matrix for High Order Finite Element Approximation on Tetrahedra

Mark Ainsworth, Shuai Jiang, 2021, SIAM J. Sci. Comput..

Mass Conserving Mixed hp-FEM Approximations to Stokes Flow. Part I: Uniform Stability

Mark Ainsworth, Charles Parker, 2021, SIAM J. Numer. Anal..

A Mass Conserving Mixed hp-FEM Scheme for Stokes Flow. Part III: Implementation and Preconditioning pdf

Mark Ainsworth, Charles Parker, M. Ainsworth, 2021, SIAM J. Numer. Anal..

Online data analysis and reduction: An important Co-design motif for extreme-scale computers

Franck Cappello, Scott Klasky, Sheng Di, 2021, The international journal of high performance computing applications.

Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control

Mark Ainsworth, Justin Dong, M. Ainsworth, 2021, SIAM J. Sci. Comput..

Mass Conserving Mixed hp-FEM Approximations to Stokes Flow. Part II: Optimal Convergence

Mark Ainsworth, Charles Parker, 2021, SIAM J. Numer. Anal..

Preconditioning high order H2 conforming finite elements on triangles

Mark Ainsworth, Charles Parker, M. Ainsworth, 2021, Numerische Mathematik.

Identification and a posteriori estimation of transported errors in finite element analysis

Mark Ainsworth, 1999 .

Technical Note: A note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes

Mark Ainsworth, Richard Rankin, M. Ainsworth, 2012 .

Recovery‐Based Error Estimators

J. Tinsley Oden, Mark Ainsworth, 2011 .

Diagonal scaling of stiffness matrices in the Galerkin boundary element method

Mark Ainsworth, Thanh Tran, M. Ainsworth, 2000, The ANZIAM Journal.

Computable error bounds for nonconforming Fortin–Soulie finite element approximation of the Stokes problem

Mark Ainsworth, Gabriel R. Barrenechea, Alejandro Allendes, 2012 .

Post-processing with computable error bounds for the finite element approximation of a nonlinear heat conduction problem

Mark Ainsworth, Ian H. Sloan, Song Wang, 1997 .

Guaranteed computable bounds on quantities of interest in finite element computations

Mark Ainsworth, Richard Rankin, M. Ainsworth, 2012 .

Hierarchic finite element bases on unstructured tetrahedral meshes

Mark Ainsworth, Joe Coyle, J. Coyle, 2003 .

Solution of elastic scattering problems in linear acoustics using h-p boundary element methods

Mark Ainsworth, Leszek Demkowicz, J. T. Oden, 1991 .

Explicit polynomial preserving trace liftings on a triangle

Mark Ainsworth, Leszek Demkowicz, 2009 .

Bernstein-Bézier finite elements on tetrahedral–hexahedral–pyramidal partitions

Larry L. Schumaker, Mark Ainsworth, Oleg Davydov, 2016 .

A Posteriori Error Estimators for the Stokes and Oseen Equations

J. Tinsley Oden, Mark Ainsworth, J. Oden, 1997 .

Reliable and Robust A Posteriori Error Estimation for Singularly Perturbed Reaction-Diffusion Problems

Ivo Babuška, Mark Ainsworth, I. Babuska, 1999 .

Computation of Maxwell eigenvalues on curvilinear domains using hp -version Nédélec elements

Mark Ainsworth, Joe Coyle, J. Coyle, 2003 .

Realistic computable error bounds for three dimensional finite element analyses in linear elasticity

Mark Ainsworth, Richard Rankin, M. Ainsworth, 2011 .

A uniformly stable family of mixed hp‐finite elements with continuous pressures for incompressible flow

Mark Ainsworth, Patrick Coggins, 2002 .

Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains

Mark Ainsworth, Christian Glusa, 2018 .

A Synthesis of A Posteriori Error Estimation Techniques for Conforming , Non-Conforming and Discontinuous Galerkin Finite Element Methods

Mark Ainsworth, M. Ainsworth, 2005 .

A unified Petrov-Galerkin spectral method for fractional PDEs

Mark Ainsworth, George Em Karniadakis, Mohsen Zayernouri, 2015 .

Hierarchic hp-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes

Mark Ainsworth, Joe Coyle, J. Coyle, 2001 .

Wavelets, multilevel methods and elliptic PDEs

Mark Ainsworth, M. Ainsworth, 1997 .

Well-posedness of the Cahn–Hilliard equation with fractional free energy and its Fourier Galerkin approximation

Mark Ainsworth, Zhiping Mao, M. Ainsworth, 2017 .

A Preconditioner Based on Domain Decomposition for H-P Finite-Element Approximation on Quasi-Uniform Meshes

Mark Ainsworth, M. Ainsworth, 1996 .

Topics in Computational Wave Propagation

Mark Ainsworth, Bryan P. Rynne, Dugald B. Duncan, 2003 .

Aspects of an adaptive finite element method for the fractional Laplacian: A priori and a posteriori error estimates, efficient implementation and multigrid solver☆☆☆

Mark Ainsworth, Christian Glusa, Christian A. Glusa, 2017, 1708.03912.

Fully computable a posteriori error bounds for stabilised FEM approximations of convection–reaction–diffusion problems in three dimensions

Mark Ainsworth, Gabriel R. Barrenechea, Alejandro Allendes, 2013 .

Fractional phase-field crystal modelling: analysis, approximation and pattern formation

Mark Ainsworth, Zhiping Mao, M. Ainsworth, 2020 .

The Conditioning of Boundary Element Equations on Locally Refined Meshes and Preconditioning by Diagonal Scaling

Mark Ainsworth, Thanh Tran, William McLean, 1999 .

The hp-MITC finite element method for the Reissner-Mindlin plate problem

Mark Ainsworth, Katia Pinchedez, 2002 .

Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods

Mark Ainsworth, M. Ainsworth, 2004 .

Analysis of Iterative Sub-structuring Techniques for Boundary Element Approximation of the Hypersingular Operator in Three Dimensions

Mark Ainsworth, Benqi Guo, 2002 .

A Bernstein–Bézier Basis for Arbitrary Order Raviart–Thomas Finite Elements

Mark Ainsworth, Oleg Davydov, Gaelle Andriamaro, 2015 .

An adaptive multi‐scale approach to the modelling of masonry structures

Mark Ainsworth, Loredana Angela Mihai, M. Ainsworth, 2009 .

An adaptive refinement strategy for hp -finite element computations

Mark Ainsworth, M. Ainsworth, B. Senior, 1998 .

A posteriori error estimators for second order elliptic systems: Part 1. Theoretical foundations and a posteriori error analysis

J. Tinsley Oden, Mark Ainsworth, J. Oden, 1993 .

A posteriori error estimators for second order elliptic systems part 2. An optimal order process for calculating self-equilibrating fluxes

Mark Ainsworth, J. T. Oden, J. Oden, 1993 .

Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes

Mark Ainsworth, Richard Rankin, 2011 .

Approximation theory for the hp -version finite element method and application to the non-linear Laplacian

Mark Ainsworth, David Kay, 2000 .

Local a posteriori error estimators for variational inequalities

J. Tinsley Oden, Mark Ainsworth, J. Oden, 1993 .

Explicit discrete dispersion relations for the acoustic wave equation in d-dimensions using finite element, spectral element and optimally blended schemes

Mark Ainsworth, Hafiz Abdul Wajid, M. Ainsworth, 2010 .

Semi-discrete Galerkin approximation of the single layer equation by general splines

Mark Ainsworth, Ian H. Sloan, Rolf Dieter Grigorieff, 1998 .

A posteriori error estimation for non-conforming quadrilateral finite elements

Mark Ainsworth, 2005 .

A posteriori error estimation in the finite element method

Mark Ainsworth, 1989 .

Bernstein–Bézier bases for tetrahedral finite elements

Mark Ainsworth, Guosheng Fu, M. Ainsworth, 2018, Computer Methods in Applied Mechanics and Engineering.

Domain decomposition preconditioners for p and hp finite element approximation of Stokes equations

Mark Ainsworth, Spencer J. Sherwin, S. Sherwin, 1999 .