A note on the efficient evaluation of a modified Hilbert transformation

DOI10.1515/jnma-2019-0099zbMath1471.65154OpenAlexW3041894191MaRDI QIDQ2025328

Marco Zank, Olaf Steinbach

Publication date: 12 May 2021

Published in: Journal of Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jnma-2019-0099

zbMATH Keywords

heat equationspace-time FEMmodified Hilbert transformation

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Heat equation (35K05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for integral transforms (65R10) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items

Towards coercive boundary element methods for the wave equation, Exponential convergence of hp-time-stepping in space-time discretizations of parabolic PDES, Integral representations and quadrature schemes for the modified Hilbert transformation, A note on a modified Hilbert transform, Space-time methods for time-dependent partial differential equations. Abstracts from the workshop held February 6--12, 2022, An exact realization of a modified Hilbert transformation for space-time methods for parabolic evolution equations, Efficient Direct Space-Time Finite Element Solvers for Parabolic Initial-Boundary Value Problems in Anisotropic Sobolev Spaces

Uses Software

• hlib
• GitHub

Cites Work

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• Efficient numerical methods for non-local operators. \(\mathcal H^2\)-matrix compression, algorithms and analysis.
• Hierarchical matrices. A means to efficiently solve elliptic boundary value problems
• The construction of some efficient preconditioners in the boundary element method
• Coercive space-time finite element methods for initial boundary value problems
• The fast solution of boundary integral equations.
• Hierarchical Matrices: Algorithms and Analysis
• Numerical Approximation Methods for Elliptic Boundary Value Problems
• Fractional Space-Time Variational Formulations of (Navier--) Stokes Equations
• Petrov–Galerkin space-time hp-approximation of parabolic equations in H1/2
• Boundary Element Methods