4.5 Article

ROBUST BPX PRECONDITIONER FOR FRACTIONAL LAPLACIANS ON BOUNDED LIPSCHITZ DOMAINS

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Mathematics

Besov regularity for the Dirichlet integral fractional Laplacian in Lipschitz domains

Juan Pablo Borthagaray et al.

JOURNAL OF FUNCTIONAL ANALYSIS (2022)

Article Mathematics, Applied

ON THE STABILITY OF SCOTT-ZHANG TYPE OPERATORS AND APPLICATION TO MULTILEVEL PRECONDITIONING IN FRACTIONAL DIFFUSION

Markus Faustmann et al.

Summary: The article provides an endpoint stability result for Scott-Zhang type operators in Besov spaces, showing that these operators are bounded from H-3/2 into B-2,infinity(3/2) for globally continuous piecewise polynomials, and from H-1/2 into B-2,infinity(1/2) for element wise polynomials. An application of this result is a multilevel decomposition based on Scott-Zhang operators on a hierarchy of meshes generated by newest vertex bisection, with an exclusion of the endpoint case. Additionally, a local multilevel diagonal preconditioner for the fractional Laplacian on locally refined meshes with optimal eigenvalue bounds is presented.

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS (2021)

Article Mathematics, Applied

QUASI-OPTIMAL CONVERGENCE RATE FOR AN ADAPTIVE METHOD FOR THE INTEGRAL FRACTIONAL LAPLACIAN

Markus Faustmann et al.

Summary: This study introduces a reliable weighted residual a posteriori error estimator for the discretization of the integral fractional Laplacian, and proves optimal convergence rates for an h-adaptive algorithm driven by this error estimator. The key lies in the local inverse estimates for the fractional Laplacian, which are crucial for the analysis of the adaptive algorithm.

MATHEMATICS OF COMPUTATION (2021)

Article Mathematics, Applied

Optimal operator preconditioning for pseudodifferential boundary problems

Heiko Gimperlein et al.

Summary: In this paper, an operator preconditioner for general elliptic pseudodifferential equations is proposed, achieving condition numbers independent of mesh size and choice of bases in low-order Galerkin discretizations. The study provides a unified and independent proof for specific cases of operators, emphasizing the increasing relevance of mesh regularity assumptions with the order of the operator. Numerical examples validate theoretical findings and demonstrate the performance of the proposed preconditioner on various types of meshes.

NUMERISCHE MATHEMATIK (2021)

Article Mathematics, Applied

LOCAL ENERGY ESTIMATES FOR THE FRACTIONAL LAPLACIAN

Juan Pablo Borthagaray et al.

Summary: The study focuses on the impact of the fractional Laplace operator on solutions to the Dirichlet problem and its performance in finite element discretizations. It is shown that the approximation error is mainly concentrated near the boundary of the domain, and this is illustrated through numerical examples.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2021)

Article Mathematics, Applied

Uniform preconditioners for problems of positive order

Rob Stevenson et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2020)

Article Engineering, Multidisciplinary

Space-time adaptive finite elements for nonlocal parabolic variational inequalities

Heiko Gimperlein et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2019)

Article Mathematics, Applied

H-matrix approximability of inverses of discretizations of the fractional Laplacian

Michael Karkulik et al.

ADVANCES IN COMPUTATIONAL MATHEMATICS (2019)

Article Mathematics, Applied

Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian

Juan Pablo Borthagaray et al.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2019)

Article Mathematics, Applied

MULTIGRID METHODS FOR DISCRETE FRACTIONAL SOBOLEV SPACES

Trygve Baerland et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2019)

Article Mathematics, Applied

Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations

Matteo Bonforte et al.

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS (2018)

Article Mathematics, Interdisciplinary Applications

Numerical methods for fractional diffusion

Andrea Bonito et al.

COMPUTING AND VISUALIZATION IN SCIENCE (2018)

Article Mathematics, Applied

A FRACTIONAL LAPLACE EQUATION: REGULARITY OF SOLUTIONS AND FINITE ELEMENT APPROXIMATIONS

Gabriel Acosta et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2017)

Article Engineering, Multidisciplinary

Aspects of an adaptive finite element method for the fractional Laplacian: A priori and a posteriori error estimates, efficient implementation and multigrid solver

Mark Ainsworth et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2017)

Article Engineering, Multidisciplinary

Adaptive finite element method for fractional differential equations using hierarchical matrices

Xuan Zhao et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2017)

Article Mathematics, Applied

Uniform convergence of multigrid methods for adaptive meshes

Jinbiao Wu et al.

APPLIED NUMERICAL MATHEMATICS (2017)

Article Mathematics, Applied

INTERPOLATION OF HILBERT AND SOBOLEV SPACES: QUANTITATIVE ESTIMATES AND COUNTEREXAMPLES

S. N. Chandler-Wilde et al.

MATHEMATIKA (2015)

Article Mathematics, Applied

The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary

Xavier Ros-Oton et al.

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES (2014)

Article Mathematics, Applied

Analysis of the Scott-Zhang interpolation in the fractional order Sobolev spaces

P. Ciarlet

JOURNAL OF NUMERICAL MATHEMATICS (2013)

Article Mathematics, Applied

A CONVERGENT ADAPTIVE FINITE ELEMENT ALGORITHM FOR NONLOCAL DIFFUSION AND PERIDYNAMIC MODELS

Qiang Du et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2013)

Article Mathematics, Applied

Hitchhiker's guide to the fractional Sobolev spaces

Eleonora Di Nezza et al.

BULLETIN DES SCIENCES MATHEMATIQUES (2012)

Article Mathematics, Applied

Optimal multilevel methods for graded bisection grids

Long Chen et al.

NUMERISCHE MATHEMATIK (2012)

Article Mathematics

The best constant in a fractional Hardy inequality

Krzysztof Bogdan et al.

MATHEMATISCHE NACHRICHTEN (2011)

Article Mathematics, Applied

A posteriori error analysis for a class of integral equations and variational inequalities

Ricardo H. Nochetto et al.

NUMERISCHE MATHEMATIK (2010)

Article Multidisciplinary Sciences

Scaling laws of marine predator search behaviour

David W. Sims et al.

NATURE (2008)

Article Mathematics

Two-sided eigenvalue estimates for subordinate processes in domains

ZQ Chen et al.

JOURNAL OF FUNCTIONAL ANALYSIS (2005)

Article Environmental Sciences

Application of a fractional advection-dispersion equation

DA Benson et al.

WATER RESOURCES RESEARCH (2000)