Sobolev Regularity Estimation for hp-Adaptive Finite Element Methods

By Paul Houston, B. Senior, Endre Süli. 2003

79 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2a511f3a1b8ab9b9e41bec72823f79d03f2a7e93

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In Computational Mechanics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

A Survey of hp-Adaptive Strategies for Elliptic Partial Differential Equations (2011, unknown): “[15] present the other two approaches which use the Legendre coefficients to estimate the regularity of the solution.”
A posteriori error analysis of hp-version discontinuous Galerkin finite-element methods for second-order quasi-linear elliptic PDEs (2007, methodology): “To this end, we employ the hp-adaptive strategy developed in [28], where the local regularity of the analytical solution is estimated from truncated local Legendre expansions of the computed numerical solution; see, also, [16, 26].”
An adaptive strategy for hp-FEM based on testing for analyticity (2007, background): “This idea was first discussed in [24] (see also [22, 21 ]).”
hp-Version discontinuous Galerkin methods with interior penalty for partial differential equations with nonnegative characteristic form. (2002, methodology): “In this final example we consider the performance of our hp–adaptive algorithm for the (symmetric) version of the interior penalty method applied to a nonlinear problem; the extension of the above Type I a posteriori error analysis to the case of a nonlinear convection–diffusion problem follows dire”
Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality (2002, unknown): “…to h- or p-refine, based on the Sobolev smoothness estimation strategy proposed in Ainsworth and Senior (1998) in the context of hp-adaptive norm control for second-order elliptic problems; for a review of recent developments on Sobolev regularity estimation, we refer to Houston and Süli (2002a).”
Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics (2011, methodology): “In high-order methods, additional strategies include p-adaptation, in which the approximation order is changed on a fixed triangulation [40] [86], and hp-adaptation in which both the order and the triangulation are varied [87] [88] [89] [90] [91] [92] [93] [94] [95] [96].”