D-Index & Metrics Best Publications

D-Index & Metrics

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 56 Citations 10,726 179 World Ranking 344 National Ranking 185
Mechanical and Aerospace Engineering D-index 51 Citations 8,898 155 World Ranking 346 National Ranking 179

Research.com Recognitions

Awards & Achievements

2009 - THE J. TINSLEY ODEN MEDAL For pioneering work in both the theory and implementation of hp-Finite Element Methods, its application to numerous areas of computational mechanics, and in particular to computational electromagnetics

2002 - Fellow of the International Association for Computational Mechanics (IACM)

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Finite element method
  • Geometry

His scientific interests lie mostly in Finite element method, Mathematical analysis, Applied mathematics, Boundary value problem and Mathematical optimization. In his research, Leszek Demkowicz undertakes multidisciplinary study on Finite element method and Electromagnetism. His Mathematical analysis research incorporates themes from Petrov–Galerkin method and Robustness.

In his work, Smoothed finite element method and Boundary knot method is strongly intertwined with Extended finite element method, which is a subfield of Applied mathematics. In his study, Calculus is inextricably linked to Partial differential equation, which falls within the broad field of Boundary value problem. His work carried out in the field of Mathematical optimization brings together such families of science as Perfectly matched layer, Interpolation error, Interpolation and Frequency domain.

His most cited work include:

  • Toward a universal h-p adaptive finite element strategy, part 1. Constrained approximation and data structure (377 citations)
  • Toward a universal h-p adaptive finite element strategy, part 2. A posteriori error estimation (354 citations)
  • Computing with hp-ADAPTIVE FINITE ELEMENTS : Volume 1 One and Two Dimensional Elliptic and Maxwell Problems (264 citations)

What are the main themes of his work throughout his whole career to date?

His main research concerns Finite element method, Mathematical analysis, Applied mathematics, Maxwell's equations and Polygon mesh. His Finite element method study integrates concerns from other disciplines, such as Discretization, Numerical analysis and Mathematical optimization. The concepts of his Mathematical analysis study are interwoven with issues in Linear elasticity, Petrov–Galerkin method and Galerkin method.

His research integrates issues of Grid, Geometry and Calculus in his study of Applied mathematics. His studies in Maxwell's equations integrate themes in fields like Compact space and Exact sequence. Leszek Demkowicz focuses mostly in the field of Polygon mesh, narrowing it down to topics relating to Solver and, in certain cases, Algorithm and Computational science.

He most often published in these fields:

  • Finite element method (54.44%)
  • Mathematical analysis (37.41%)
  • Applied mathematics (24.81%)

What were the highlights of his more recent work (between 2014-2021)?

  • Applied mathematics (24.81%)
  • Finite element method (54.44%)
  • Mathematical analysis (37.41%)

In recent papers he was focusing on the following fields of study:

Leszek Demkowicz focuses on Applied mathematics, Finite element method, Mathematical analysis, Petrov–Galerkin method and Discretization. His Applied mathematics research includes elements of Factorization, Singular perturbation and Polygon mesh. He is studying Stiffness matrix, which is a component of Finite element method.

His Mathematical analysis study combines topics in areas such as Wave propagation, Linear elasticity and Ideal. The Petrov–Galerkin method study combines topics in areas such as Mathematical physics, Mathematical optimization, Least squares, Extended finite element method and Discontinuous Galerkin method. He combines subjects such as Numerical analysis and Partial differential equation with his study of Discretization.

Between 2014 and 2021, his most popular works were:

  • Breaking spaces and forms for the DPG method and applications including Maxwell equations (104 citations)
  • Orientation embedded high order shape functions for the exact sequence elements of all shapes (62 citations)
  • The DPG methodology applied to different variational formulations of linear elasticity (33 citations)

In his most recent research, the most cited papers focused on:

  • Mathematical analysis
  • Geometry
  • Algebra

His primary scientific interests are in Mathematical analysis, Applied mathematics, Finite element method, Polygon mesh and A priori and a posteriori. His Mathematical analysis research incorporates elements of Linear elasticity, Petrov–Galerkin method and Computation. Leszek Demkowicz has researched Applied mathematics in several fields, including Iterative method, Preconditioner, Solver and Conjugate gradient method.

His Finite element method study combines topics from a wide range of disciplines, such as Operator, Differential operator and Schrödinger equation. The various areas that Leszek Demkowicz examines in his Polygon mesh study include Grid, Convection–diffusion equation, Hermitian matrix and Bounding overwatch. His Discretization research is multidisciplinary, relying on both Positive-definite matrix, Mesh generation, Numerical analysis and Viscoelasticity.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Computing with hp-ADAPTIVE FINITE ELEMENTS : Volume 1 One and Two Dimensional Elliptic and Maxwell Problems

Leszek Demkowicz.
(2006)

967 Citations

Toward a universal h-p adaptive finite element strategy, part 1. Constrained approximation and data structure

L. Demkowicz;J.T. Oden;W. Rachowicz;O. Hardy.
Computer Methods in Applied Mechanics and Engineering (1989)

577 Citations

Toward a universal h-p adaptive finite element strategy, part 2. A posteriori error estimation

J.T. Oden;L. Demkowicz;W. Rachowicz;T.A. Westermann.
Computer Methods in Applied Mechanics and Engineering (1989)

543 Citations

Applied functional analysis

J. Tinsley Oden;Leszek F. Demkowicz.
(1996)

506 Citations

Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume II Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications

Leszek Demkowicz;Jason Kurtz;David Pardo;Maciej Paszynski.
(2007)

377 Citations

Toward a universal adaptive finite element strategy part 3. design of meshes

W. Rachowicz;J.T. Oden;L. Demkowicz.
Computer Methods in Applied Mechanics and Engineering (1989)

287 Citations

A class of discontinuous Petrov–Galerkin methods. II. Optimal test functions

Leszek Demkowicz;Jay Gopalakrishnan.
Numerical Methods for Partial Differential Equations (2011)

284 Citations

A Fully Automatic hp -Adaptivity

L. Demkowicz;W. Rachowicz;Ph. Devloo.
Journal of Scientific Computing (2002)

260 Citations

A class of discontinuous Petrov-Galerkin methods. Part III

Leszek Demkowicz;Jay Gopalakrishnan;Antti H. Niemi.
Applied Numerical Mathematics (2012)

225 Citations

A Class of Discontinuous Petrov–Galerkin Methods. Part I: The Transport Equation

Leszek Demkowicz;Jay Gopalakrishnan.
Computer Methods in Applied Mechanics and Engineering (2010)

225 Citations

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