H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 81 Citations 19,978 343 World Ranking 63 National Ranking 1

Research.com Recognitions

Awards & Achievements

2016 - SIAM Fellow For contributions to the theory and computational methods for partial differential equations.

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Statistics
  • Partial differential equation

Christoph Schwab focuses on Mathematical analysis, Finite element method, Discretization, Rate of convergence and Galerkin method. His Mathematical analysis study incorporates themes from Tensor product and Discontinuous Galerkin method. His work on Constitutive equation as part of general Finite element method study is frequently linked to A domain, bridging the gap between disciplines.

His Discretization research incorporates elements of Tensor, Order, Elliptic curve, Elliptic operator and Incompressible flow. His Rate of convergence research is multidisciplinary, incorporating perspectives in Basis, Algorithm, Sparse matrix and Bounded function. His Galerkin method study integrates concerns from other disciplines, such as Combinatorics, Domain, Stiffness matrix, Eigenvalues and eigenvectors and Piecewise.

His most cited work include:

  • Boundary Element Methods (599 citations)
  • Discontinuous hp -Finite Element Methods for Advection-Diffusion-Reaction Problems (396 citations)
  • P- and hp- finite element methods : theory and applications in solid and fluid mechanics (318 citations)

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

Christoph Schwab spends much of his time researching Mathematical analysis, Applied mathematics, Finite element method, Discretization and Galerkin method. Christoph Schwab interconnects Rate of convergence, Tensor product and Discontinuous Galerkin method in the investigation of issues within Mathematical analysis. His study in Applied mathematics is interdisciplinary in nature, drawing from both Parametric statistics, Uncertainty quantification, Quasi-Monte Carlo method, Mathematical optimization and Monte Carlo method.

His biological study spans a wide range of topics, including Degree of a polynomial, Numerical analysis and Polygon mesh. His studies in Discretization integrate themes in fields like Estimator and Random field. His studies deal with areas such as Boundary element method, Stiffness matrix, Integral equation and Piecewise as well as Galerkin method.

He most often published in these fields:

  • Mathematical analysis (53.64%)
  • Applied mathematics (31.19%)
  • Finite element method (25.99%)

What were the highlights of his more recent work (between 2015-2021)?

  • Applied mathematics (31.19%)
  • Mathematical analysis (53.64%)
  • Uncertainty quantification (8.52%)

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

Christoph Schwab mainly focuses on Applied mathematics, Mathematical analysis, Uncertainty quantification, Parametric statistics and Bounded function. The various areas that Christoph Schwab examines in his Applied mathematics study include Bayes estimator, Finite element method, Quasi-Monte Carlo method, Random field and Discretization. His research integrates issues of Monte Carlo method, Partial differential equation and Linear subspace in his study of Discretization.

Christoph Schwab combines subjects such as Rate of convergence, Navier–Stokes equations and Discontinuous Galerkin method with his study of Mathematical analysis. Christoph Schwab has researched Parametric statistics in several fields, including Affine transformation, Banach space, Petrov–Galerkin method, Parametrization and Bayesian probability. His Bounded function research integrates issues from Pure mathematics, Tensor product, Sobolev space and hp-FEM.

Between 2015 and 2021, his most popular works were:

  • Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ (71 citations)
  • Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems (46 citations)
  • DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing (41 citations)

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

  • Mathematical analysis
  • Statistics
  • Algebra

His primary scientific interests are in Applied mathematics, Parametric statistics, Mathematical analysis, Uncertainty quantification and Quasi-Monte Carlo method. His Applied mathematics research is multidisciplinary, incorporating elements of Banach space, Finite element method, Separable space, Estimator and Mathematical optimization. Christoph Schwab has included themes like Bayes estimator, Bayesian probability, Affine transformation, Petrov–Galerkin method and Discretization in his Parametric statistics study.

Christoph Schwab is interested in Partial differential equation, which is a field of Mathematical analysis. His Uncertainty quantification research is multidisciplinary, relying on both Parameter space and Visualization. His research in Quasi-Monte Carlo method intersects with topics in Covariance and Random field.

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.

Top Publications

P- and hp- finite element methods : theory and applications in solid and fluid mechanics

Ch. Schwab.
(1998)

1169 Citations

Boundary Element Methods

Stefan A. Sauter;Christoph Schwab.
(2010)

833 Citations

Discontinuous hp -Finite Element Methods for Advection-Diffusion-Reaction Problems

Paul Houston;Christoph Schwab;Endre Süli.
SIAM Journal on Numerical Analysis (2001)

608 Citations

Finite elements for elliptic problems with stochastic coefficients

Philipp Frauenfelder;Christoph Schwab;Radu Alexandru Todor.
Computer Methods in Applied Mechanics and Engineering (2005)

433 Citations

Karhunen-Loève approximation of random fields by generalized fast multipole methods

Christoph Schwab;Radu Alexandru Todor.
Journal of Computational Physics (2006)

388 Citations

Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients

Andrea Barth;Christoph Schwab;Nathaniel Zollinger.
Numerische Mathematik (2011)

348 Citations

ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S

Albert Cohen;Ronald Devore;Christoph Schwab.
Analysis and Applications (2011)

336 Citations

Convergence Rates of Best N -term Galerkin Approximations for a Class of Elliptic sPDEs

Albert Cohen;Ronald DeVore;Christoph Schwab.
Foundations of Computational Mathematics (2010)

303 Citations

Local Discontinuous Galerkin Methods for the Stokes System

Bernardo Cockburn;Guido Kanschat;Dominik Schötzau;Christoph Schwab.
SIAM Journal on Numerical Analysis (2002)

276 Citations

Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients

Radu Alexandru Todor;Christoph Schwab.
Ima Journal of Numerical Analysis (2007)

275 Citations

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking h-index is inferred from publications deemed to belong to the considered discipline.

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