A fully adaptive wavelet algorithm for parabolic partial differential equations

DOI10.1016/S0168-9274(00)00016-7zbMath0973.65089OpenAlexW2055556299MaRDI QIDQ5928469

Guillaume Chiavassa, Jacques Liandrat

Publication date: 4 July 2001

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

Full work available at URL: https://doi.org/10.1016/s0168-9274(00)00016-7

zbMATH Keywords

heat equationnumerical experimentsparabolic equationBurgers equationswavelet algorithm

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Heat equation (35K05) Numerical methods for wavelets (65T60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (11)

A comparison of the finite difference and multiresolution method for the elliptic equations with Dirichlet boundary conditions on irregular domains ⋮ A smooth fictitious domain/multiresolution method for elliptic equations on general domains ⋮ The existence and uniqueness of solution to wavelet collocation ⋮ A study of multiscale wavelet-based elements for adaptive finite element analysis ⋮ A multiresolution prewavelet-based adaptive refinement scheme for RBF approximations of nearly singular problems ⋮ Operator-adapted wavelets for finite-element differential forms ⋮ Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients ⋮ Coupling wavelets/vaguelets and smooth fictitious domain methods for elliptic problems: the univariate case ⋮ DEFINITION AND ANALYSIS OF A WAVELET/FICTITIOUS DOMAIN SOLVER FOR THE 2D-HEAT EQUATION ON A GENERAL DOMAIN ⋮ Two adaptive wavelet algorithms for nonlinear parabolic partial differential equations ⋮ On coupling wavelets with fictitious domain approaches

Cites Work

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• On the effective construction of compactly supported wavelets satisfying homogeneous boundary conditions on the interval
• Spectral and finite difference solutions of the Burgers equations
• On the fast approximation of some nonlinear operators in nonregular wavelet spaces
• A pseudo-wavelet scheme for the two-dimensional Navier-Stokes equation
• On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases
• Numerical simulation of decaying turbulence in an adaptive wavelet basis
• Fast wavelet transforms and numerical algorithms I
• Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R)
• Fourier Analysis of the Finite Element Method in Ritz‐Galerkin Theory

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