NDLI: Quasi-optimality of adaptive finite element methods for controlling local energy errors

Please wait, while we are loading the content...

Numerische Mathematik : Volume 136

Numerische Mathematik : Volume 135

Numerische Mathematik : Volume 134

Numerische Mathematik : Volume 134, Issue 4, December 2016

Numerische Mathematik : Volume 134, Issue 3, November 2016

Numerische Mathematik : Volume 134, Issue 2, October 2016

Numerische Mathematik : Volume 134, Issue 1, September 2016

Justification of the saturation assumption

Quasi-optimality of adaptive finite element methods for controlling local energy errors

Strong and weak convergence order of finite element methods for stochastic PDEs with spatial white noise

Additive average Schwarz method for a Crouzeix–Raviart finite volume element discretization of elliptic problems with heterogeneous coefficients

Long-term analysis of the Störmer–Verlet method for Hamiltonian systems with a solution-dependent high frequency

Unconditional stability and error estimates of modified characteristics FEMs for the Navier–Stokes equations

Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions

Residual-based a posteriori error estimation for multipoint flux mixed finite element methods

Numerische Mathematik : Volume 133

Numerische Mathematik : Volume 89

Quasi-optimality of adaptive finite element methods for controlling local energy errors

Content Provider	Springer Nature Link
Author	Demlow, Alan
Copyright Year	2015
Abstract	A rich theory demonstrating convergence and optimality of adaptive finite element methods (AFEM) has been developed in recent years. In this work we prove optimality of AFEM which are designed to control local energy errors in elliptic partial differential equations. Because errors propagate globally in FEM, controlling local errors requires controlling both local energy solution properties and global error contributions (pollution errors) which may be measured in a weaker norm such as the $$L_2$$ norm. We define adaptive methods which control both of these error components and prove that they converge with the best possible rate over all possible refinements of the initial mesh. These results are valid for Poisson’s problem on convex polyhedral domains in arbitrary space dimension. Our theory establishes AFEM optimality for several adaptive marking strategies which rigorously control pollution effects. We also present numerical examples that illustrate our theory and confirm that local energy AFEM without pollution control can fail to yield optimal meshes.
Ending Page	60
Page Count	34
Starting Page	27
File Format	PDF
ISSN	0029599X
e-ISSN	09453245
Journal	Numerische Mathematik
Issue Number	1
Volume Number	134
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-10-31
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	ApplicationMathematics/Computational Methods of Engineering Mathematical Methods in Physics Numerical Analysis Theoretical, Mathematical and Computational Physics Numerical and Computational Physics Mathematics Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Convergence of an Adaptive Finite Element Method for Controlling Local Energy Errors

Discontinuous Petrov–Galerkin boundary elements

Local two-sided bounds for eigenvalues of self-adjoint operators

How Many Numerical Eigenvalues Can We Trust?

Quasi-Optimality of Adaptive Nonconforming Finite Element Methods for the Stokes Equations

Justification of the saturation assumption

Adaptive finite element method for elliptic optimal control problems: convergence and optimality

An Adaptive FEM for a Maxwell Interface Problem

Convergence and optimality of $${\mathbf {hp}}$$ -AFEM

Quasi-optimality of adaptive finite element methods for controlling local energy errors

Similar Documents

Convergence of an Adaptive Finite Element Method for Controlling Local Energy Errors

Discontinuous Petrov–Galerkin boundary elements

Local two-sided bounds for eigenvalues of self-adjoint operators

How Many Numerical Eigenvalues Can We Trust?

Quasi-Optimality of Adaptive Nonconforming Finite Element Methods for the Stokes Equations

Justification of the saturation assumption

Adaptive finite element method for elliptic optimal control problems: convergence and optimality

An Adaptive FEM for a Maxwell Interface Problem

Convergence and optimality of $${\mathbf {hp}}$$ -AFEM

Quasi-optimality of adaptive finite element methods for controlling local energy errors