A wavelet Galerkin method for the Stokes equations

DOI10.1007/BF02238515zbMath0849.65077OpenAlexW1608434507MaRDI QIDQ1913350

Angela Kunoth, Karsten Urban, Wolfgang Dahmen

Publication date: 3 November 1996

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02238515

zbMATH Keywords

waveletsmultiresolution analysisnumerical experimentssaddle point problemspreconditionersStokes equationsSchur complementsLadyšenskaja-Babuška-Brezzi conditionGalerkin schemes

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Numerical computation of matrix norms, conditioning, scaling (65F35) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items

Adaptive wavelet methods for saddle point problems, Second-generation wavelet optimized finite difference method (SGWOFD) for solution of Burger’s equation with different boundary conditions, Anisotropic multiscale systems on bounded domains, Enhanced MultiResolution Analysis for MultiDimensional Data Utilizing Line Filtering Techniques, A wavelet-like Galerkin method for numerical solution of variational inequalities arising in elastoplasticity, Are Adaptive Galerkin Schemes Dissipative?, Wavelet Galerkin scheme for solving nonlinear dispersive shallow water waves: application in bore propagation and breaking, Wavelet bases in $\mathbf{H}( \mathrm{div})$ and $\mathbf{H}(\mathbf{curl})$, WAVELET-BASED ADAPTIVE COLLOCATION METHOD FOR THE RESOLUTION OF NONLINEAR PDEs, Stabilized wavelet approximations of the Stokes problem, Spectral graph wavelet optimized finite difference method for solution of Burger's equation with different boundary conditions, Homogeneous Dirichlet wavelets on the interval diagonalizing the derivative operator, and application to free-slip divergence-free wavelets, Stable multiscale bases and local error estimation for elliptic problems, Approximation properties of hybrid shearlet-wavelet frames for Sobolev spaces, Wavelet methods for PDEs -- some recent developments, Recent results on wavelet bases on the interval generated by GP refinable functions, Solution of Cartesian and curvilinear quantum equations via multiwavelets on the interval, Using divergence-free wavelets for the numerical solution of the 2-D stationary Navier-Stokes equations, A Matlab suite for second generation wavelets on an interval and the corresponding adaptive grid, SIGNAL ANALYSIS AND PERFORMANCE EVALUATION OF A VEHICLE CRASH TEST WITH A FIXED SAFETY BARRIER BASED ON HAAR WAVELETS, Biorthogonal spline wavelets on the interval -- stability and moment conditions, The wavelet element method. I: Construction and analysis, Galerkin meshfree methods: a review and mathematical implementation aspects, Divergence-free and curl-free wavelets in two dimensions and three dimensions: application to turbulent flows, Stable multiscale discretizations for saddle point problems and preconditioning

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Iterative techniques for time dependent Stokes problems
• Fonctions à support compact dans les analyses multi-résolutions. (Functions of compact support in multi-resolution analysis)
• Multilevel preconditioning
• Nonorthogonal multiresolution analyses, commutation between projectors and differentiation and divergence-free vector wavelets
• A stability criterion for biorthogonal wavelet bases and their related subband coding scheme
• A practical guide to splines
• Biorthogonal spline wavelets on the interval -- stability and moment conditions
• Wavelets on the interval and fast wavelet transforms
• Biorthogonal multiresolution analysis on the interval and applications
• On divergence-free wavelets
• Multilevel preconditioning -- appending boundary conditions by Lagrange multipliers
• Parallel Multilevel Preconditioners
• Finite Element Methods for Navier-Stokes Equations
• Stationary subdivision
• Biorthogonal bases of compactly supported wavelets
• An analysis of the convergence of mixed finite element methods
• Using the Refinement Equation for Evaluating Integrals of Wavelets
• Finite elements. Theory, fast solvers and applications in elasticity theory