On approximation classes for adaptive time-stepping finite element methods
نویسندگان
چکیده
Abstract We study approximation classes for adaptive time-stepping finite element methods time-dependent partial differential equations. measure the error in $L_2([0,T)\times \varOmega )$ and consider with discontinuous elements time continuous space, of any degree. As a by-product we define anisotropic Besov spaces Banach-space-valued functions on an interval derive some embeddings, as well Jackson- Whitney-type estimates.
منابع مشابه
Approximation classes for adaptive higher order finite element approximation
The following small mistakes where found in [GM] and the corresponding corrections should be introduced: • Statement of Proposition 2.1 (page 2129); statement of Theorem 2.2 (page 2130): replace s+ α ≤ r + 1 τ∗ by s+ α < r + 1. • Second line of Section 4.2 (page 2142), replace s < r+ max{1, 1 p} = r+ 1 p∗ by s < r + 1. • Remark 4.8 (page 2143): Replace s < r′ + max{1, 1 p} by s < r ′ + 1. • Rem...
متن کاملAdaptive Finite Element Methods
In the numerical solution of practical problems of physics or engineering such as, e.g., computational fluid dynamics, elasticity, or semiconductor device simulation one often encounters the difficulty that the overall accuracy of the numerical approximation is deteriorated by local singularities such as, e.g., singularities arising from re-entrant corners , interior or boundary layers, or shar...
متن کاملAdaptive Finite Element Methods
Adaptive methods are now widely used in the scientific computation to achieve better accuracy with minimum degree of freedom. In this chapter, we shall briefly survey recent progress on the convergence analysis of adaptive finite element methods (AFEMs) for second order elliptic partial differential equations and refer to Nochetto, Siebert and Veeser [14] for a detailed introduction to the theo...
متن کاملAdaptive Finite Element Methods for Multiphysics Problems Adaptive Finite Element Methods for Multiphysics Problems
In this thesis we develop and evaluate the performance of adaptive finite element methods for multiphysics problems. In particular, we propose a methodology for deriving computable error estimates when solving unidirectionally coupled multiphysics problems using segregated finite element solvers. The error estimates are of a posteriori type and are derived using the standard framework of dual w...
متن کاملAdaptive Space-Time Finite Element Methods for Parabolic Optimization Problems
In this paper we summerize recent results on a posteriori error estimation and adaptivity for space-time finite element discretizations of parabolic optimization problems. The provided error estimates assess the discretization error with respect to a given quantity of interest and separate the influences of different parts of the discretization (time, space, and control discretization). This al...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ima Journal of Numerical Analysis
سال: 2022
ISSN: ['1464-3642', '0272-4979']
DOI: https://doi.org/10.1093/imanum/drac056