Skip to content
DraconiticResearch
Search Sources API
182,544 studies31 sourcesUpdated 1 h ago
PreprintarXiv licencearXiv

Extending a new two-grid waveform relaxation on a spatial finite element discretization

  • A. Mesforush
  • N. Habibi
Open at sourcePDFDOICite

Abstract

In this work, a new two-grid method presented for the elliptic partial differential equations is generalized to the time-dependent linear parabolic partial differential equations. The new two-grid waveform relaxation method uses the numerical method of lines, replacing any spatial derivative by a discrete formula, obtained here by the finite element method. A convergence analysis in terms of the spectral radius of the corresponding two-grid waveform relaxation operator is also developed. Moreover, the efficiency of the presented method and its analysis are tested, applying the two-dimensional heat equation.

Related

  1. Neumann-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay
    Deeksha Tomer
    arXivPreprintarXiv licenceFull textAnalysis & PDEsNumerical analysis & scientific computingarXiv
  2. Dirichlet-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay in Multiple Subdomains
    Bankim Chandra Mandal, Deeksha Tomer
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  3. Dirichlet--Neumann waveform relaxation for heterogeneous heat equations: fully discrete l2 analysis
    Philipp Birken, Niklas Kotarsky
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv
  4. A dual-field structure-preserving mixed finite element discretization for incompressible Hall MHD equations
    Yi Zhang
    arXivPreprintarXiv licenceFull textMathematical physicsNumerical analysis & scientific computingarXiv
  5. Study of the finite element discretization of the iterated quasi-reversibility method The Laplacian data assimilation case
    Jérémi Dardé, Jérémy Heleine
    HALPreprintCC BY-NC-SA 4.0Full textNumerical analysis & scientific computingOptimisation & controlHALarXiv

Cite

BibTeXRIS
BibTeX
@misc{mesforush2026extending,
  title = {{Extending a new two-grid waveform relaxation on a spatial finite element discretization}},
  author = {A. Mesforush and N. Habibi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27935},
  eprint = {2609.27935},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27935},
}
RIS
TY  - UNPB
TI  - Extending a new two-grid waveform relaxation on a spatial finite element discretization
AU  - A. Mesforush
AU  - N. Habibi
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.27935
UR  - https://arxiv.org/abs/2609.27935
AB  - In this work, a new two-grid method presented for the elliptic partial differential equations is generalized to the time-dependent linear parabolic partial differential equations. The new two-grid waveform relaxation method uses the numerical method of lines, replacing any spatial derivative by a discrete formula, obtained here by the finite element method. A convergence analysis in terms of the spectral radius of the corresponding two-grid waveform relaxation operator is also developed. Moreover, the efficiency of the presented method and its analysis are tested, applying the two-dimensional heat equation.
ER  -