Weighted Error Estimates for Transient Transport Problems Discretized Using Continuous Finite Elements with Interior Penalty Stabilization on the Gradient Jumps

JOURNAL ARTICLE published October 2022 in Vietnam Journal of Mathematics

Research funded by Engineering and Physical Sciences Research Council (EP/P01576X/1) | Engineering and Physical Sciences Research Council (EP/T033126/1)

Authors: Erik Burman

Pointwise error estimates for 𝐶⁰ interior penalty approximation of biharmonic problems

JOURNAL ARTICLE published 8 October 2020 in Mathematics of Computation

Research funded by National Science Foundation (1913133)

Authors: D. Leykekhman

Uniform error estimates in the finite element method for a singularly perturbed reaction-diffusion problem

JOURNAL ARTICLE published 1 January 2008 in Mathematics of Computation

Authors: Dmitriy Leykekhman

Supercloseness of the continuous interior penalty method for singularly perturbed problems in 1D: Vertex-cell interpolation

JOURNAL ARTICLE published January 2018 in Applied Numerical Mathematics

Research funded by National Science Foundation of China (11771257) | Shandong Provincial Natural Science Foundation, China (ZR2017MA003) | A Project of Shandong Province Higher Educational Science and Technology Program (J17KA169) | National Science Foundation of China (11601251) | Shandong Provincial Natural Science Foundation, China (ZR2016AM13) | A Project of Shandong Province Higher Educational Science and Technology Program (J16LI10)

Authors: Jin Zhang | Xiaowei Liu

A posteriori error estimates for a dual finite element method for singularly perturbed reaction–diffusion problems

JOURNAL ARTICLE published March 2024 in BIT Numerical Mathematics

Research funded by National Science Foundation (DMS-2208289) | National Natural Science Foundation of China (12171025,NSAF-U2230402)

Authors: JaEun Ku | Martin Stynes

Error Estimates of the Finite Element Method with Weighted Basis Functions for a Singularly Perturbed Convection-Diffusion Equation

JOURNAL ARTICLE published June 2011 in Journal of Computational Mathematics

Authors: Xianggui Li

Global error estimates for a uniparametric family of stiffly accurate Runge-Kutta collocation methods on singularly perturbed problems

JOURNAL ARTICLE published March 2011 in BIT Numerical Mathematics

Authors: S. González-Pinto | D. Hernández-Abreu

A continuous interior penalty finite element method for a third-order singularly perturbed boundary value problem

JOURNAL ARTICLE published March 2018 in Computational and Applied Mathematics

Research funded by Ministry of Education, Science and Technological Development of the Republic of Serbia (174030,174030)

Authors: Helena Zarin | Hans-Görg Roos | Ljiljana Teofanov

Layers and corner singularities in singularly perturbed elliptic problems

JOURNAL ARTICLE published June 2008 in BIT Numerical Mathematics

Authors: R. Bruce Kellogg | Martin Stynes

Pointwise Error Estimates for the LDG Method Applied to 1-d Singularly Perturbed Reaction-Diffusion Problems

JOURNAL ARTICLE published 1 January 2013 in Computational Methods in Applied Mathematics

Authors: Huiqing Zhu | Zhimin Zhang

Supercloseness analysis of the nonsymmetric interior penalty Galerkin method for a singularly perturbed problem on Bakhvalov-type mesh

JOURNAL ARTICLE published October 2023 in Applied Mathematics Letters

Research funded by National Natural Science Foundation of China (11771257) | Natural Science Foundation of Shandong Province (ZR2021MA004)

Authors: Xiaoqi Ma | Jin Zhang

Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra

JOURNAL ARTICLE published 1 March 2012 in Mathematics of Computation

Authors: J. Guzmán | D. Leykekhman

A posteriori error estimates by recovered gradients in parabolic finite element equations

JOURNAL ARTICLE published September 2008 in BIT Numerical Mathematics

Authors: D. Leykekhman | L. B. Wahlbin

A Priori and a Posteriori Error Estimates of a Weakly Over-Penalized Interior Penalty Method for Non-Self-Adjoint and Indefinite Problems

JOURNAL ARTICLE published June 2014 in Journal of Computational Mathematics

Authors: Yuping Zeng

Balanced-norm error estimates for sparse grid finite element methods applied to singularly perturbed reaction–diffusion problems

JOURNAL ARTICLE published 26 March 2019 in Journal of Numerical Mathematics

Authors: Stephen Russell | Martin Stynes

Recurrence Method for Solving Singularly Perturbed Boundary Value Problems

JOURNAL ARTICLE published November 2010 in Studies in Applied Mathematics

Authors: B. Lin | K. Li | Z. Cheng

Continuous Interior Penalty hp-Finite Element Methods for Transport Operators

BOOK CHAPTER published in Numerical Mathematics and Advanced Applications

Authors: Erik Burman | Alexandre Ern

Non-Symmetric Interior Penalty Galerkin Finite Element Method for a Class of Singularly Perturbed Reaction Diffusion Problems with Discontinuous Data

JOURNAL ARTICLE published December 2022 in International Journal of Applied and Computational Mathematics

Research funded by Council for Scientific and Industrial research, India (09/045(1547)/2017-EMR-I) | Science and Engineering Research Board, DST, India (SPG/2022/000063)

Authors: Ram Prasad Yadav | Pratima Rai | Kapil K. Sharma

Optimal error estimate of upwind scheme on Shishkin-type meshes for singularly perturbed parabolic problems with discontinuous convection coefficients

JOURNAL ARTICLE published June 2011 in BIT Numerical Mathematics

Authors: Kaushik Mukherjee | Srinivasan Natesan

Superconvergence analysis of a finite element method for a two-parameter singularly perturbed problem

JOURNAL ARTICLE published December 2009 in BIT Numerical Mathematics

Authors: Ljiljana Teofanov | Helena Zarin