What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Partial differential equation
- Statistics
Anthony T. Patera spends much of his time researching Mathematical analysis, Partial differential equation, Applied mathematics, Basis and Numerical analysis.
In his research on the topic of Mathematical analysis, Spectral method is strongly related with Finite element method.
His work carried out in the field of Partial differential equation brings together such families of science as Projection, Nonlinear system, Pressure-correction method and Affine transformation.
His Applied mathematics study combines topics in areas such as Nearest-neighbor interpolation, Birkhoff interpolation, Spline interpolation, Interpolation and Mathematical optimization.
His Basis research integrates issues from Estimator, Parametric statistics and Galerkin method.
His study looks at the intersection of Numerical analysis and topics like Parameter space with Eigenvalues and eigenvectors.
His most cited work include:
- A spectral element method for fluid dynamics: Laminar flow in a channel expansion (1628 citations)
- An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations (926 citations)
- Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations (816 citations)
What are the main themes of his work throughout his whole career to date?
Anthony T. Patera mostly deals with Mathematical analysis, Partial differential equation, Applied mathematics, Finite element method and Basis.
His Mathematical analysis study incorporates themes from Navier–Stokes equations, Domain decomposition methods and Nonlinear system.
He has included themes like Projection, Numerical analysis and Affine transformation in his Partial differential equation study.
His Applied mathematics study combines topics from a wide range of disciplines, such as Upper and lower bounds, Estimator, Mathematical optimization and Residual.
His Finite element method research incorporates themes from Discretization, Helmholtz equation and Heat transfer.
His study in Basis is interdisciplinary in nature, drawing from both Parametric statistics and Galerkin method.
He most often published in these fields:
- Mathematical analysis (33.67%)
- Partial differential equation (29.65%)
- Applied mathematics (28.64%)
What were the highlights of his more recent work (between 2011-2020)?
- Applied mathematics (28.64%)
- A priori and a posteriori (16.08%)
- Basis (22.11%)
In recent papers he was focusing on the following fields of study:
Applied mathematics, A priori and a posteriori, Basis, Partial differential equation and Mathematical analysis are his primary areas of study.
His research in Applied mathematics intersects with topics in Reduction, Greedy algorithm, Residual, Space and Function.
His Basis study integrates concerns from other disciplines, such as Element, Dimension and Reduction.
The study incorporates disciplines such as Algorithm, Helmholtz free energy, Finite element method and Model order reduction in addition to Partial differential equation.
The concepts of his Finite element method study are interwoven with issues in Discretization and Elliptic partial differential equation, Nonlinear system.
His work on Interpolation and Inverse Laplace transform as part of general Mathematical analysis study is frequently linked to Gauss–Jacobi quadrature, Gaussian quadrature and Gauss–Kronrod quadrature formula, therefore connecting diverse disciplines of science.
Between 2011 and 2020, his most popular works were:
- A PRIORI CONVERGENCE OF THE GREEDY ALGORITHM FOR THE PARAMETRIZED REDUCED BASIS METHOD (199 citations)
- An improved error bound for reduced basis approximation of linear parabolic problems (77 citations)
- A Static condensation Reduced Basis Element method: approximation and a posteriori error estimation (77 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Statistics
- Partial differential equation
Anthony T. Patera focuses on Applied mathematics, A priori and a posteriori, Mathematical analysis, Partial differential equation and Greedy algorithm.
His Applied mathematics research includes elements of Reduction and Domain decomposition methods.
His study of A priori and a posteriori brings together topics like Basis, Mathematical optimization, Discretization, Parametric statistics and Acoustics.
His studies in Mathematical optimization integrate themes in fields like Estimator and Bounded function.
Anthony T. Patera has researched Mathematical analysis in several fields, including Bilinear interpolation and Constant.
His work deals with themes such as Helmholtz free energy, Representation and Data mining, which intersect with Partial differential equation.
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