2014 - SIAM Fellow For contributions to numerical analysis and scientific computing including finite element methods, adaptive methods, reliability, and a posteriori error estimation.
His primary scientific interests are in Finite element method, Applied mathematics, Mathematical analysis, Numerical analysis and Estimator. His work in the fields of Finite element method, such as Mixed finite element method and Discontinuous Galerkin method, intersects with other areas such as A priori and a posteriori. His Applied mathematics study incorporates themes from Discretization, Mathematical optimization and Boundary value problem.
His Mathematical analysis research is multidisciplinary, incorporating elements of Dispersion relation, Condition number and Galerkin method. His work carried out in the field of Numerical analysis brings together such families of science as Spectral method, Algorithm, Adaptive method, Finite element algorithm and System of linear equations. The Norm study combines topics in areas such as Finite element approximations, Thrust and Nonlinear system.
Mark Ainsworth spends much of his time researching Finite element method, Applied mathematics, Mathematical analysis, Estimator and A priori and a posteriori. The study incorporates disciplines such as Upper and lower bounds, Numerical analysis, Partial differential equation and Polygon mesh in addition to Finite element method. His Applied mathematics research incorporates themes from Boundary value problem, Norm, Mathematical optimization, Discretization and Discontinuous Galerkin method.
His work deals with themes such as Multigrid method and Round-off error, which intersect with Mathematical optimization. His Mathematical analysis study integrates concerns from other disciplines, such as Condition number and Galerkin method. His Estimator research is multidisciplinary, relying on both Residual, Finite element approximations and Calculus.
The scientist’s investigation covers issues in Applied mathematics, Finite element method, Mathematical analysis, Reduction and Compression. By researching both Applied mathematics and A priori and a posteriori, Mark Ainsworth produces research that crosses academic boundaries. His research in Finite element method intersects with topics in Partial differential equation, Mass matrix, Stability and Mathematical physics.
His Mathematical analysis research includes elements of Tetrahedron, Polygon mesh and Unit cube. His Reduction study combines topics from a wide range of disciplines, such as Visualization and Data reduction. Mark Ainsworth has researched Norm in several fields, including Upper and lower bounds, Vector field, Finite element approximations and Estimator.
His scientific interests lie mostly in Boundary, Reduction, Compression, Algorithm and Applied mathematics. His studies deal with areas such as Laplacian smoothing, Mixed finite element method, Partial differential equation, Stiffness matrix and Sparse approximation as well as Boundary. The various areas that Mark Ainsworth examines in his Reduction study include Univariate, Representation, Range and Flexibility.
His Flexibility research focuses on Visualization and how it connects with Computer architecture and Computational complexity theory. His Applied mathematics research integrates issues from Boundary value problem, Bounded function, Discretization, Function and Domain. His Boundary value problem research includes themes of Equivalence, Numerical analysis and Collocation.
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A Posteriori Error Estimation in Finite Element Analysis
Mark Ainsworth;J.Tinsley Oden.
A Posteriori Error Estimation in Finite Element Analysis: Oden/A Posteriori
Mark Ainsworth;J. Tinsley Oden.
A unified approach to a posteriori error estimation using element residual methods
Mark Ainsworth;J. Tinsley Oden.
Numerische Mathematik (1993)
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
Journal of Computational Physics (2004)
Discrete Dispersion Relation for hp -Version Finite Element Approximation at High Wave Number
SIAM Journal on Numerical Analysis (2004)
Dispersive and Dissipative Properties of Discontinuous Galerkin Finite Element Methods for the Second-Order Wave Equation
M. Ainsworth;P. Monk;W. Muniz.
Journal of Scientific Computing (2006)
Analysis of the Zienkiewicz–Zhu a‐posteriori error estimator in the finite element method
M. Ainsworth;J. Z. Zhu;A. W. Craig;O. C. Zienkiewicz.
International Journal for Numerical Methods in Engineering (1989)
Hierarchic finite element bases on unstructured tetrahedral meshes
Mark Ainsworth;Joe Coyle.
International Journal for Numerical Methods in Engineering (2003)
Aspects of an adaptive hp-finite element method : Adaptive strategy, conforming approximation and efficient solvers
Mark Ainsworth;Bill Senior.
Computer Methods in Applied Mechanics and Engineering (1997)
What is the fractional Laplacian? A comparative review with new results
Anna Lischke;Guofei Pang;Mamikon A. Gulian;Fangying Song.
Journal of Computational Physics (2020)
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