NDLI: Discontinuous Galerkin Methods Based on Weighted Interior Penalties for Second Order PDEs with Non-smooth Coefficients

Content Provider	Springer Nature Link
Author	Zuni, Paolo
Copyright Year	2008
Abstract	We develop and analyze a Discontinuous Galerkin (DG) method based on weighted interior penalties (WIP) applied to second order (elliptic) PDEs and in particular to advection-diffusion-reaction equations featuring non-smooth and possibly vanishing diffusivity. First of all, looking at the derivation of a DG scheme with a bias to domain decomposition methods, we carefully discuss the set up of the discretization scheme in a general framework putting into evidence the helpful role of the weights and the connection with the well known Local Discontinuous Galerkin schemes (LDG). Then, we address the a-priori error analysis of the method, recovering optimal error estimates in suitable norms. By virtue of the introduction of the weighted penalties, these results turn out to be robust with respect to the diffusion parameter. Furthermore, we discuss the derivation of an a-posteriori local error indicator suitable for advection-diffusion-reaction problems with highly variable, locally small diffusivity. All the theoretical results are illustrated and discussed by means of numerical experiments.
Starting Page	99
Ending Page	126
Page Count	28
File Format	PDF
ISSN	08857474
Journal	Journal of Scientific Computing
Volume Number	38
Issue Number	1
e-ISSN	15737691
Language	English
Publisher	Springer US
Publisher Date	2008-07-17
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Advection-diffusion-reaction equations Discontinuous Galerkin Interior penalties A-priori and a-posteriori error analysis Mathematical and Computational Physics ApplicationMathematics/Computational Methods of Engineering Computational Mathematics and Numerical Analysis Algorithms
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Engineering Computational Theory and Mathematics Computational Mathematics Numerical Analysis Software

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

A posteriori energy-norm error estimates for advection-diffusion equations approximated by weighted interior penalty methods

A posteriori energy-norm error estimates for advection-diffusion equations approximated by weighted interior penalty methods

Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection

A-Posteriori Error Estimates for Discontinuous Galerkin Approximations of Second Order Elliptic Problems

A Posteriori Error Estimation for Interior Penalty Finite Element Approximations of the Advection-Reaction Equation

Residual-based a posteriori error estimates for hp-discontinuous Galerkin discretisations of the biharmonic problem

Hp-Version a priori Error Analysis of Interior Penalty Discontinuous Galerkin Finite Element Approximations to the Biharmonic Equation

A Posteriori Local Discontinuous Galerkin Error Estimation for Two-Dimensional Convection–Diffusion Problems

Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems

Discontinuous Galerkin Methods Based on Weighted Interior Penalties for Second Order PDEs with Non-smooth Coefficients

Similar Documents

A posteriori energy-norm error estimates for advection-diffusion equations approximated by weighted interior penalty methods

A posteriori energy-norm error estimates for advection-diffusion equations approximated by weighted interior penalty methods

Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection

A-Posteriori Error Estimates for Discontinuous Galerkin Approximations of Second Order Elliptic Problems

A Posteriori Error Estimation for Interior Penalty Finite Element Approximations of the Advection-Reaction Equation

Residual-based a posteriori error estimates for hp-discontinuous Galerkin discretisations of the biharmonic problem

Hp-Version a priori Error Analysis of Interior Penalty Discontinuous Galerkin Finite Element Approximations to the Biharmonic Equation

A Posteriori Local Discontinuous Galerkin Error Estimation for Two-Dimensional Convection–Diffusion Problems

Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems

Discontinuous Galerkin Methods Based on Weighted Interior Penalties for Second Order PDEs with Non-smooth Coefficients