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Nonlinear and adaptive frame approximation schemes for elliptic PDEs: Theory and numerical experiments

https://doi.org/10.1002/num.20407
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Biorthogonal bases of compactly supported wavelets
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Wavelets on the Interval and Fast Wavelet Transforms
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Local Decomposition of Refinable Spaces and Wavelets
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The Wavelet Element Method
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Biorthogonal Spline Wavelets on the Interval—Stability and Moment Conditions
inferredcites →https://doi.org/10.1007/3-540-29960-2openalex-snapshot
Angewandte Funktionalanalysis
inferredcites →https://doi.org/10.1007/978-3-0348-8619-2_4openalex-snapshot
Wavelets on a Bounded Interval
inferredcites →https://doi.org/10.1007/bf02476032openalex-snapshot
Schrödinger equation and oscillatory Hilbert transforms of second degree
inferredcites →https://doi.org/10.1007/bf03322055openalex-snapshot
Wavelets with Complementary Boundary Conditions — Function Spaces on the Cube
inferredcites →https://doi.org/10.1007/pl00005404openalex-snapshot
Wavelet adaptive method for second order elliptic problems: boundary conditions and domain decomposition
inferredcites →https://doi.org/10.1007/s00211-007-0127-5openalex-snapshot
Adaptive frame methods for nonlinear variational problems
inferredcites →https://doi.org/10.1007/s10444-005-7501-6openalex-snapshot
Adaptive frame methods for elliptic operator equations
inferredcites →https://doi.org/10.1016/j.acha.2004.01.004openalex-snapshot
Bi-framelet systems with few vanishing moments characterize Besov spaces
inferredcites →https://doi.org/10.1016/j.jat.2009.04.001openalex-snapshot
Optimal adaptive computations in the Jaffard algebra and localized frames
inferredcites →https://doi.org/10.1016/s0168-9274(96)00060-8openalex-snapshot
Stable multiscale bases and local error estimation for elliptic problems
inferredcites →https://doi.org/10.1016/s0893-9659(99)00075-0openalex-snapshot
Besov regularity for elliptic boundary value problems in polygonal domains
inferredcites →https://doi.org/10.1016/s1570-8659(00)07004-6openalex-snapshot
Wavelet methods in numerical analysis
inferredcites →https://doi.org/10.1016/s1570-8659(13)70047-4openalex-snapshot
Handbook of Numerical Analysis
inferredcites →https://doi.org/10.1016/s1874-608x(97)80008-8openalex-snapshot
Nonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations
inferredcites →https://doi.org/10.1017/s0962492900002816openalex-snapshot
Nonlinear approximation
inferredcites →https://doi.org/10.1090/s0002-9947-96-01501-2openalex-snapshot
A Multivariate Faa di Bruno Formula with Applications
inferredcites →https://doi.org/10.1090/s0025-5718-00-01252-7openalex-snapshot
Adaptive wavelet methods for elliptic operator equations: Convergence rates
inferredcites →https://doi.org/10.1090/s0025-5718-06-01828-xopenalex-snapshot
Wavelets on manifolds: An optimized construction
inferredcites →https://doi.org/10.1090/s0025-5718-06-01867-9openalex-snapshot
Wavelets with patchwise cancellation properties
inferredcites →https://doi.org/10.1090/s0025-5718-99-01092-3openalex-snapshot
Composite wavelet bases for operator equations
inferredcites →https://doi.org/10.1093/imanum/drl035openalex-snapshot
Adaptive frame methods for elliptic operator equations: the steepest descent approach
inferredcites →https://doi.org/10.1093/imanum/drm025openalex-snapshot
Computation of differential operators in aggregated wavelet frame coordinates
inferredcites →https://doi.org/10.1137/060651021openalex-snapshot
Composite Wavelet Bases with Extended Stability and Cancellation Properties
inferredcites →https://doi.org/10.1137/1.9781611972030openalex-snapshot
Elliptic Problems in Nonsmooth Domains
inferredcites →https://doi.org/10.1137/s0036141002411520openalex-snapshot
On the Compressibility of Operators in Wavelet Coordinates
inferredcites →https://doi.org/10.1137/s0036141098333451openalex-snapshot
Wavelets on Manifolds I: Construction and Domain Decomposition
inferredcites →https://doi.org/10.1137/s0036142902407988openalex-snapshot
Adaptive Solution of Operator Equations Using Wavelet Frames
inferredcites →https://doi.org/10.1137/s0895479801397858openalex-snapshot
Spectral Analysis of the Transition Operator and Its Applications to Smoothness Analysis of Wavelets
inferredcites →https://doi.org/10.1137/s1064827599365501openalex-snapshot
Adaptive Wavelet Schemes for Elliptic Problems---Implementation and Numerical Experiments
inferredcites →https://doi.org/10.1142/2802openalex-snapshot
Approximation Theory VIII
inferredcites →https://doi.org/10.1142/s0219691308002422openalex-snapshot
ON THE COMPUTATION OF GRAMIAN MATRICES FOR REFINABLE BASES ON THE INTERVAL
inferredcites →https://doi.org/10.1515/9783110812411openalex-snapshot
Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations
inferredcites →https://doi.org/10.17192/z2007.0343openalex-snapshot
Adaptive Wavelet- und Frame-Verfahren für elliptische und parabolische Gleichungen
inferredcites →https://doi.org/10.2307/2003660openalex-snapshot
International Series of Numerical Mathematics
inferredcites →https://doi.org/10.2307/2007301openalex-snapshot
Spline Functions: Basic Theory.

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1002/zamm.201300096openalex-snapshot
Besov regularity for the Stokes and the Navier‐Stokes system in polyhedral domains
inferred← citeshttps://doi.org/10.1007/978-3-642-03596-8_9openalex-snapshot
Compressive Algorithms—Adaptive Solutions of PDEs and Variational Problems
inferred← citeshttps://doi.org/10.1007/s00025-008-0352-yopenalex-snapshot
Biorthogonal Cubic Hermite Spline Multiwavelets on the Interval with Complementary Boundary Conditions
inferred← citeshttps://doi.org/10.1007/s00025-009-0008-6openalex-snapshot
New Stable Biorthogonal Spline-Wavelets on the Interval
inferred← citeshttps://doi.org/10.1007/s00211-007-0127-5openalex-snapshot
Adaptive frame methods for nonlinear variational problems
inferred← citeshttps://doi.org/10.1007/s00211-013-0572-2openalex-snapshot
Adaptive wavelet methods for elliptic partial differential equations with random operators
inferred← citeshttps://doi.org/10.1007/s10444-010-9152-5openalex-snapshot
Construction of optimally conditioned cubic spline wavelets on the interval
inferred← citeshttps://doi.org/10.1007/s10444-016-9503-yopenalex-snapshot
Numerical approaches to the functional distribution of anomalous diffusion with both traps and flights
inferred← citeshttps://doi.org/10.1007/s10444-019-09679-9openalex-snapshot
Approximation properties of hybrid shearlet-wavelet frames for Sobolev spaces
inferred← citeshttps://doi.org/10.1016/j.jat.2009.04.001openalex-snapshot
Optimal adaptive computations in the Jaffard algebra and localized frames
inferred← citeshttps://doi.org/10.1080/00036811.2010.504184openalex-snapshot
Adaptive frame methods for nonlinear elliptic problems
inferred← citeshttps://doi.org/10.1090/mcom/2009-78-266openalex-snapshot
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A multiplicative Schwarz adaptive wavelet method for elliptic boundary value problems
inferred← citeshttps://doi.org/10.1093/imanum/draa030openalex-snapshot
Adaptive quarkonial domain decomposition methods for elliptic partial differential equations
inferred← citeshttps://doi.org/10.48550/arxiv.1505.01012openalex-snapshot
Applications of Wavelet Bases to The Numerical Solutions of Fractional PDEs
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