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 45 Citations 9,213 130 World Ranking 755 National Ranking 50
Engineering and Technology D-index 42 Citations 7,963 95 World Ranking 2284 National Ranking 168

Research.com Recognitions

Awards & Achievements

2015 - SIAM Fellow For contributions to the numerical analysis of nonlinear partial differential equations.

1990 - SPIE Fellow

1988 - Fellow of the Royal Society, United Kingdom

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Quantum mechanics
  • Partial differential equation

His scientific interests lie mostly in Mathematical analysis, Finite element method, Cahn–Hilliard equation, Numerical analysis and Partial differential equation. His Mathematical analysis study combines topics in areas such as Mean curvature and Geometry. His Finite element method research includes themes of Discretization, Surface, Attractor and Kinetics.

His study in Surface is interdisciplinary in nature, drawing from both Conservation law, Mechanics and Simulation. His Cahn–Hilliard equation research includes elements of Conservation of mass, Perturbation, Galerkin method, Backward Euler method and Space. His Numerical analysis research integrates issues from Iterative method, Uniqueness and Extended finite element method.

His most cited work include:

  • On the Cahn-Hilliard equation (456 citations)
  • Weak and variational methods for moving boundary problems (381 citations)
  • Finite element methods for surface PDEs (370 citations)

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

Charles M. Elliott spends much of his time researching Mathematical analysis, Finite element method, Surface, Numerical analysis and Applied mathematics. His work on Mathematical analysis deals in particular with Partial differential equation, Uniqueness, Free boundary problem, Boundary value problem and Cahn–Hilliard equation. His research integrates issues of Discretization, Variational inequality and Geometry in his study of Finite element method.

His research investigates the connection between Surface and topics such as Domain that intersect with issues in Hilbert space. His Numerical analysis research focuses on Statistical physics and how it relates to Superconductivity. His Applied mathematics study incorporates themes from Class, Elliptic partial differential equation, Dirichlet distribution and Regularization.

He most often published in these fields:

  • Mathematical analysis (58.38%)
  • Finite element method (34.59%)
  • Surface (24.32%)

What were the highlights of his more recent work (between 2016-2021)?

  • Surface (24.32%)
  • Applied mathematics (16.76%)
  • Discretization (11.89%)

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

Surface, Applied mathematics, Discretization, Mathematical analysis and Finite element method are his primary areas of study. The concepts of his Surface study are interwoven with issues in Space, Uniqueness and Domain. His Applied mathematics research is multidisciplinary, incorporating perspectives in Logarithm, Elliptic partial differential equation and Energy functional.

The Discretization study combines topics in areas such as Regularization, Computation and Torus. Charles M. Elliott has included themes like Geodesic curvature and Phase in his Mathematical analysis study. His biological study spans a wide range of topics, including Inverse problem, Finite difference, Boundary value problem, Optimization problem and Eikonal equation.

Between 2016 and 2021, his most popular works were:

  • Small deformations of Helfrich energy minimising surfaces with applications to biomembranes (15 citations)
  • Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics (15 citations)
  • A coupled ligand-receptor bulk-surface system on a moving domain : well posedness, regularity and convergence to equilibrium (10 citations)

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

  • Quantum mechanics
  • Mathematical analysis
  • Partial differential equation

The scientist’s investigation covers issues in Surface, Uniqueness, Mathematical analysis, Applied mathematics and Discretization. His Surface research incorporates themes from Classical mechanics, Field, Finite element method and Domain. Charles M. Elliott has researched Finite element method in several fields, including Unified field theory, Numerical analysis, Function space and Bilinear form.

Mathematical analysis is a component of his Parabolic partial differential equation and Partial differential equation studies. His research in Applied mathematics intersects with topics in Hypersurface, Monotone polygon, Elliptic partial differential equation and Approximation theory. His studies deal with areas such as Deformation, Computation, Torus and Finite volume method as well as Discretization.

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

Weak and variational methods for moving boundary problems

Charles M. Elliott;J. R Ockendon.
(1982)

714 Citations

On the Cahn-Hilliard equation

Charles M. Elliott;Zheng Songmu.
Archive for Rational Mechanics and Analysis (1986)

623 Citations

On the Cahn-Hilliard equation with degenerate mobility

Charles M. Elliott;Harald Garcke.
Siam Journal on Mathematical Analysis (1996)

480 Citations

Finite element methods for surface PDEs

Gerhard Dziuk;Charles M. Elliott.
Acta Numerica (2013)

424 Citations

Computation of geometric partial differential equations and mean curvature flow

Klaus Deckelnick;Gerhard Dziuk;Charles M Elliott.
Acta Numerica (2005)

419 Citations

Finite elements on evolving surfaces

G. Dziuk;C. M. Elliott.
Ima Journal of Numerical Analysis (2007)

368 Citations

The Cahn-Hilliard Model for the Kinetics of Phase Separation

C. M. Elliott.
(1989)

317 Citations

The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature

J. W. Cahn;C. M. Elliott;A. Novick-Cohen.
European Journal of Applied Mathematics (1996)

316 Citations

Numerical Studies of the Cahn-Hilliard Equation for Phase Separation

Charles M. Elliott;Donald A. French.
Ima Journal of Applied Mathematics (1987)

315 Citations

The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysis

J. F. Blowey;C. M. Elliott.
European Journal of Applied Mathematics (1991)

290 Citations

Editorial Boards

IMA Journal of Numerical Analysis
(Impact Factor: 2.713)

Interfaces and Free Boundaries
(Impact Factor: 0.941)

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