Nonlinear approximation rates and Besov regularity for elliptic PDEs on polyhedral domains

DOI10.1007/s10208-014-9224-xzbMath1320.35126OpenAlexW1970304323MaRDI QIDQ2351808

Markus Hansen

Publication date: 26 June 2015

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/20.500.11850/154923

zbMATH Keywords

wavelet decomposition\(n\)-term approximationKondratiev spacesadaptive finite element approximation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (19)

Almost diagonal matrices and Besov-type spaces based on wavelet expansions ⋮ Regularity in Sobolev and Besov spaces for parabolic problems on domains of polyhedral type ⋮ Sobolev meets Besov: Regularity for the Poisson equation with Dirichlet, Neumann and mixed boundary values ⋮ Rate-optimal sparse approximation of compact break-of-scale embeddings ⋮ Besov estimates for weak solutions of a class of quasilinear parabolic equations with general growth ⋮ Besov regularity of inhomogeneous parabolic PDEs ⋮ An extension operator for Sobolev spaces with mixed weights ⋮ Besov regularity for operator equations on patchwise smooth manifolds ⋮ Besov regularity of solutions to the \(p\)-Poisson equation ⋮ Analytic regularity and solution approximation for a semilinear elliptic partial differential equation in a polygon ⋮ Besov regularity of parabolic and hyperbolic PDEs ⋮ Besov regularity of solutions to the \(p\)-Poisson equation in the vicinity of a vertex of a polygonal domain ⋮ Besov estimates for weak solutions of the parabolic \(p\)-Laplacian equations ⋮ On Besov regularity of solutions to nonlinear elliptic partial differential equations ⋮ Besov regularity estimates for the elliptic \(p(x)\)-Laplacian equation with the logarithmic growth ⋮ The extension problem for fractional Sobolev spaces with a partial vanishing trace condition ⋮ On the limit regularity in Sobolev and Besov scales related to approximation theory ⋮ Besov estimates for the weak solutions of a class of quasilinear elliptic equations ⋮ Spaces of Besov-Sobolev type and a problem on nonlinear approximation

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