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 40 Citations 5,812 144 World Ranking 1012 National Ranking 63
Engineering and Technology D-index 32 Citations 3,755 107 World Ranking 4503 National Ranking 160

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Thermodynamics
  • Geometry

Harald Garcke mostly deals with Mathematical analysis, Degenerate energy levels, Finite element method, Cahn–Hilliard equation and Partial differential equation. His Mathematical analysis research includes themes of Mean curvature flow and Thin-film equation. His study in Finite element method is interdisciplinary in nature, drawing from both Curvature and Discrete system.

The concepts of his Curvature study are interwoven with issues in Flow, Mixed finite element method and Numerical analysis. The various areas that he examines in his Cahn–Hilliard equation study include Bounded function, Continuum mechanics, Scaling and Diffusion equation. His work investigates the relationship between Parabolic partial differential equation and topics such as Phase transition that intersect with problems in Microstructure and Surface energy.

His most cited work include:

  • On the Cahn-Hilliard equation with degenerate mobility (369 citations)
  • Multicomponent alloy solidification: phase-field modeling and simulations. (223 citations)
  • Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities (211 citations)

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

Mathematical analysis, Flow, Finite element method, Applied mathematics and Boundary value problem are his primary areas of study. His Mathematical analysis study combines topics from a wide range of disciplines, such as Mean curvature, Mean curvature flow, Curvature, Boundary and Surface. Harald Garcke works mostly in the field of Boundary, limiting it down to topics relating to Anisotropy and, in certain cases, Stefan problem.

His study in Flow is interdisciplinary in nature, drawing from both Surface diffusion, Vector field and Balanced flow. His Finite element method research is multidisciplinary, incorporating elements of Discretization, Numerical analysis, Cahn–Hilliard equation and Free boundary problem. In his research, Topology optimization is intimately related to Optimization problem, which falls under the overarching field of Applied mathematics.

He most often published in these fields:

  • Mathematical analysis (51.28%)
  • Flow (30.77%)
  • Finite element method (20.94%)

What were the highlights of his more recent work (between 2018-2021)?

  • Mathematical analysis (51.28%)
  • Flow (30.77%)
  • Boundary value problem (12.82%)

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

Harald Garcke focuses on Mathematical analysis, Flow, Boundary value problem, Applied mathematics and Curvature. Many of his research projects under Mathematical analysis are closely connected to Degenerate energy levels with Degenerate energy levels, tying the diverse disciplines of science together. His Flow research includes elements of Distribution, Boundary, Hyperbolic geometry, Space and Elastic energy.

His research in Boundary value problem intersects with topics in Triple line, Surface diffusion and Limit. His Applied mathematics study incorporates themes from Structure, Rotational symmetry, Computation, Discretization and Numerical analysis. His Rotational symmetry research is multidisciplinary, relying on both Motion and Finite element method.

Between 2018 and 2021, his most popular works were:

  • Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis (47 citations)
  • Parametric finite element approximations of curvature-driven interface evolutions (22 citations)
  • On a Cahn--Hilliard--Brinkman Model for Tumor Growth and Its Singular Limits (21 citations)

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

  • Mathematical analysis
  • Thermodynamics
  • Geometry

His primary scientific interests are in Mathematical analysis, Flow, Curvature, Boundary value problem and Uniqueness. As part of his studies on Mathematical analysis, Harald Garcke frequently links adjacent subjects like Type. His research integrates issues of Plane and Hyperbolic geometry in his study of Flow.

His Curvature research includes themes of Numerical analysis and Finite element method. Within one scientific family, he focuses on topics pertaining to Rotational symmetry under Uniqueness, and may sometimes address concerns connected to Applied mathematics and Motion. His biological study spans a wide range of topics, including Stokes flow and Work.

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

On the Cahn-Hilliard equation with degenerate mobility

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

480 Citations

Multicomponent alloy solidification: phase-field modeling and simulations.

Britta Nestler;Harald Garcke;Björn Stinner.
Physical Review E (2005)

322 Citations

Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities

Helmut Abels;Harald Garcke;Günther Grün.
Mathematical Models and Methods in Applied Sciences (2012)

301 Citations

Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility

John W. Barrett;James F. Blowey;Harald Garcke.
SIAM Journal on Numerical Analysis (1999)

240 Citations

A multiphase field concept: numerical simulations of moving phase boundaries and multiple junctions

Harald Garcke;Britta Nestler;Barbara Stoth.
Siam Journal on Applied Mathematics (1999)

234 Citations

On a fourth-order degenerate parabolic equation: global entropy estimates, existence, and qualitative behavior of solutions

Roberta Dal Passo;Harald Garcke;Günther Grün.
Siam Journal on Mathematical Analysis (1998)

208 Citations

On anisotropic order parameter models for multi-phase system and their sharp interface limits

Harald Garcke;Britta Nestler;Barbara Stoth.
Physica D: Nonlinear Phenomena (1998)

184 Citations

A Diffuse Interface Model for Alloys with Multiple Components and Phases

Bjorn Stinner;Britta Nestler;Harald Garcke.
Siam Journal on Applied Mathematics (2004)

173 Citations

A parametric finite element method for fourth order geometric evolution equations

John W. Barrett;Harald Garcke;Robert Nürnberg.
Journal of Computational Physics (2007)

131 Citations

Parametric Approximation of Willmore Flow and Related Geometric Evolution Equations

John W. Barrett;Harald Garcke;Robert Nürnberg.
SIAM Journal on Scientific Computing (2008)

121 Citations

Editorial Boards

Interfaces and Free Boundaries
(Impact Factor: 0.941)

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