Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

A probabilistic reduced basis method for parameter-dependent problems

Marie Billaud-Friess, Arthur Macherey, Anthony Nouy and Clémentine Prieur
Advances in Computational Mathematics 50 (2) (2024)
https://doi.org/10.1007/s10444-024-10114-x

Adaptive Deep Fourier Residual method via overlapping domain decomposition

Jamie M. Taylor, Manuela Bastidas, Victor M. Calo and David Pardo
Computer Methods in Applied Mechanics and Engineering 427 116997 (2024)
https://doi.org/10.1016/j.cma.2024.116997

Multilevel Monte Carlo Methods for Stochastic Convection–Diffusion Eigenvalue Problems

Tiangang Cui, Hans De Sterck, Alexander D. Gilbert, Stanislav Polishchuk and Robert Scheichl
Journal of Scientific Computing 99 (3) (2024)
https://doi.org/10.1007/s10915-024-02539-9

An anisotropic hp-adaptation framework for ultraweak discontinuous Petrov–Galerkin formulations

Ankit Chakraborty, Stefan Henneking and Leszek Demkowicz
Computers & Mathematics with Applications 167 315 (2024)
https://doi.org/10.1016/j.camwa.2024.05.025

Learning quantities of interest from parametric PDEs: An efficient neural-weighted Minimal Residual approach

Ignacio Brevis, Ignacio Muga, David Pardo, Oscar Rodriguez and Kristoffer G. van der Zee
Computers & Mathematics with Applications 164 139 (2024)
https://doi.org/10.1016/j.camwa.2024.04.006

A study of concurrent multi-frontal solvers for modern massively parallel architectures

Jan Trynda, Maciej Woźniak and Sergio Rojas
Journal of Computational Science 75 102184 (2024)
https://doi.org/10.1016/j.jocs.2023.102184

A Deep Double Ritz Method (D2RM) for solving Partial Differential Equations using Neural Networks

Carlos Uriarte, David Pardo, Ignacio Muga and Judit Muñoz-Matute
Computer Methods in Applied Mechanics and Engineering 405 115892 (2023)
https://doi.org/10.1016/j.cma.2023.115892

SUPG-YZβ computation of chemically reactive convection-dominated nonlinear models

Süleyman Cengizci, Ömür Uğur and Srinivasan Natesan
International Journal of Computer Mathematics 100 (2) 283 (2023)
https://doi.org/10.1080/00207160.2022.2114794

An Adaptive Superconvergent Mixed Finite Element Method Based on Local Residual Minimization

Ignacio Muga, Sergio Rojas and Patrick Vega
SIAM Journal on Numerical Analysis 61 (5) 2084 (2023)
https://doi.org/10.1137/22M1526307

Isogeometric analysis and Augmented Lagrangian Galerkin Least Squares Methods for residual minimization in dual norm

Erik Burman, Peter Hansbo, Mats G. Larson and Karl Larsson
Computer Methods in Applied Mechanics and Engineering 417 116302 (2023)
https://doi.org/10.1016/j.cma.2023.116302

A reduced order modeling approach with Petrov–Galerkin projection based on hybrid snapshot simulation in Semilinear-PDEs

Feng Bai
Journal of Computational Science 67 101969 (2023)
https://doi.org/10.1016/j.jocs.2023.101969

A variational multiscale method derived from an adaptive stabilized conforming finite element method via residual minimization on dual norms

Juan F. Giraldo and Victor M. Calo
Computer Methods in Applied Mechanics and Engineering 417 116285 (2023)
https://doi.org/10.1016/j.cma.2023.116285

Solver algorithm for stabilized space-time formulation of advection-dominated diffusion problem

Marcin Łoś, Paulina Sepúlveda, Maciej Sikora and Maciej Paszyński
Computers & Mathematics with Applications 152 67 (2023)
https://doi.org/10.1016/j.camwa.2023.10.011

Subspace decomposition based DNN algorithm for elliptic type multi-scale PDEs

Xi-An Li, Zhi-Qin John Xu and Lei Zhang
Journal of Computational Physics 488 112242 (2023)
https://doi.org/10.1016/j.jcp.2023.112242

Adaptive stabilized finite elements via residual minimization onto bubble enrichments

Jose G. Hasbani, Paulina Sepúlveda, Ignacio Muga, Victor M. Calo and Sergio Rojas
Computers & Mathematics with Applications 151 1 (2023)
https://doi.org/10.1016/j.camwa.2023.09.010

Efficient discretization and preconditioning of the singularly perturbed reaction-diffusion problem

Constantin Bacuta, Daniel Hayes and Jacob Jacavage
Computers & Mathematics with Applications 109 270 (2022)
https://doi.org/10.1016/j.camwa.2022.01.031

An adaptive variational multiscale element free Galerkin method based on the residual-based a posteriori error estimators for convection–diffusion–reaction problems

Xiaoting Cao, Xiaohua Zhang and Xiaotao Shi
Engineering Analysis with Boundary Elements 136 238 (2022)
https://doi.org/10.1016/j.enganabound.2022.01.001

Subspace Decomposition Based Dnn Algorithm for Elliptic-Type Multi-Scale Pdes

Xi-An Li, Zhi-Qin John Xu and Lei Zhang
SSRN Electronic Journal (2022)
https://doi.org/10.2139/ssrn.4020731

A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems

Yu Leng, Xiaochuan Tian, Leszek Demkowicz, Hector Gomez and John T. Foster
Journal of Computational Physics 452 110919 (2022)
https://doi.org/10.1016/j.jcp.2021.110919

An anisotropic h-adaptive strategy for discontinuous Petrov-Galerkin schemes using a continuous mesh model

Ankit Chakraborty, Ajay Mandyam Rangarajan and Georg May
Computers & Mathematics with Applications 106 1 (2022)
https://doi.org/10.1016/j.camwa.2021.12.001

Nonlinear Reduced Models for State and Parameter Estimation

Albert Cohen, Wolfgang Dahmen, Olga Mula and James Nichols
SIAM/ASA Journal on Uncertainty Quantification 10 (1) 227 (2022)
https://doi.org/10.1137/20M1380818

Accuracy controlled data assimilation for parabolic problems

Wolfgang Dahmen, Rob Stevenson and Jan Westerdiep
Mathematics of Computation 91 (334) 557 (2021)
https://doi.org/10.1090/mcom/3680

Minimal residual space-time discretizations of parabolic equations: Asymmetric spatial operators

Rob Stevenson and Jan Westerdiep
Computers & Mathematics with Applications 101 107 (2021)
https://doi.org/10.1016/j.camwa.2021.09.014

Automatically adaptive stabilized finite elements and continuation analysis for compaction banding in geomaterials

Roberto J. Cier, Thomas Poulet, Sergio Rojas, Manolis Veveakis and Victor M. Calo
International Journal for Numerical Methods in Engineering 122 (21) 6234 (2021)
https://doi.org/10.1002/nme.6790

Isogeometric residual minimization (iGRM) for non-stationary Stokes and Navier–Stokes problems

M. Łoś, I. Muga, J. Muñoz-Matute and M. Paszyński
Computers & Mathematics with Applications 95 200 (2021)
https://doi.org/10.1016/j.camwa.2020.11.013

Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm

Sergio Rojas, David Pardo, Pouria Behnoudfar and Victor M. Calo
Computer Methods in Applied Mechanics and Engineering 377 113686 (2021)
https://doi.org/10.1016/j.cma.2021.113686

A stable FE method for the space-time solution of the Cahn-Hilliard equation

Eirik Valseth, Albert Romkes and Austin R. Kaul
Journal of Computational Physics 441 110426 (2021)
https://doi.org/10.1016/j.jcp.2021.110426

Robust recovery-type a posteriori error estimators for streamline upwind/Petrov Galerkin discretizations for singularly perturbed problems

Shaohong Du, Runchang Lin and Zhimin Zhang
Applied Numerical Mathematics 168 23 (2021)
https://doi.org/10.1016/j.apnum.2021.05.020

Notes on a saddle point reformulation of mixed variational problems

Constantin Bacuta, Daniel Hayes and Jacob Jacavage
Computers & Mathematics with Applications 95 4 (2021)
https://doi.org/10.1016/j.camwa.2020.07.016

Recent Advances in Least-Squares and Discontinuous Petrov–Galerkin Finite Element Methods

Fleurianne Bertrand, Leszek Demkowicz and Jay Gopalakrishnan
Computers & Mathematics with Applications 95 1 (2021)
https://doi.org/10.1016/j.camwa.2021.05.029

Automatically adaptive, stabilized finite element method via residual minimization for heterogeneous, anisotropic advection–diffusion–reaction problems

Roberto J. Cier, Sergio Rojas and Victor M. Calo
Computer Methods in Applied Mechanics and Engineering 385 114027 (2021)
https://doi.org/10.1016/j.cma.2021.114027

Stability of Galerkin discretizations of a mixed space–time variational formulation of parabolic evolution equations

Rob Stevenson and Jan Westerdiep
IMA Journal of Numerical Analysis 41 (1) 28 (2021)
https://doi.org/10.1093/imanum/drz069

Isogeometric Residual Minimization Method (iGRM) with direction splitting preconditioner for stationary advection-dominated diffusion problems

V.M. Calo, M. Łoś, Q. Deng, I. Muga and M. Paszyński
Computer Methods in Applied Mechanics and Engineering 373 113214 (2021)
https://doi.org/10.1016/j.cma.2020.113214

Discretization of Linear Problems in Banach Spaces: Residual Minimization, Nonlinear Petrov--Galerkin, and Monotone Mixed Methods

Ignacio Muga and Kristoffer G. van der Zee
SIAM Journal on Numerical Analysis 58 (6) 3406 (2020)
https://doi.org/10.1137/20M1324338

An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms

Victor M. Calo, Alexandre Ern, Ignacio Muga and Sergio Rojas
Computer Methods in Applied Mechanics and Engineering 363 112891 (2020)
https://doi.org/10.1016/j.cma.2020.112891

Eliminating Gibbs phenomena: A non-linear Petrov–Galerkin method for the convection–diffusion–reaction equation

Paul Houston, Sarah Roggendorf and Kristoffer G. van der Zee
Computers & Mathematics with Applications 80 (5) 851 (2020)
https://doi.org/10.1016/j.camwa.2020.03.025

Isogeometric Residual Minimization Method (iGRM) with direction splitting for non-stationary advection–diffusion problems

M. Łoś, J. Muñoz-Matute, I. Muga and M. Paszyński
Computers & Mathematics with Applications 79 (2) 213 (2020)
https://doi.org/10.1016/j.camwa.2019.06.023

Local meshless method for convection dominated steady and unsteady partial differential equations

Vikendra Singh, Siraj-ul-Islam and R. K. Mohanty
Engineering with Computers 35 (3) 803 (2019)
https://doi.org/10.1007/s00366-018-0632-4

An a posteriori error bound for discontinuous Galerkin approximations of convection–diffusion problems

Emmanuil H Georgoulis, Edward Hall and Charalambos Makridakis
IMA Journal of Numerical Analysis 39 (1) 34 (2019)
https://doi.org/10.1093/imanum/drx065

The Discrete-Dual Minimal-Residual Method (DDMRes) for Weak Advection-Reaction Problems in Banach Spaces

Ignacio Muga, Matthew J. W. Tyler and Kristoffer G. van der Zee
Computational Methods in Applied Mathematics 19 (3) 557 (2019)
https://doi.org/10.1515/cmam-2018-0199

A Non-conforming Saddle Point Least Squares Approach for an Elliptic Interface Problem

Constantin Bacuta and Jacob Jacavage
Computational Methods in Applied Mathematics 19 (3) 399 (2019)
https://doi.org/10.1515/cmam-2018-0202

Adaptive anisotropic Petrov–Galerkin methods for first order transport equations

Wolfgang Dahmen, Gitta Kutyniok, Wang-Q Lim, Christoph Schwab and Gerrit Welper
Journal of Computational and Applied Mathematics 340 191 (2018)
https://doi.org/10.1016/j.cam.2018.02.023

High-order polygonal discontinuous Petrov–Galerkin (PolyDPG) methods using ultraweak formulations

Ali Vaziri Astaneh, Federico Fuentes, Jaime Mora and Leszek Demkowicz
Computer Methods in Applied Mechanics and Engineering 332 686 (2018)
https://doi.org/10.1016/j.cma.2017.12.011

A DPG Framework for Strongly Monotone Operators

Pierre Cantin and Norbert Heuer
SIAM Journal on Numerical Analysis 56 (5) 2731 (2018)
https://doi.org/10.1137/18M1166663

Optimal Convergence Rates for Adaptive Lowest-Order Discontinuous Petrov--Galerkin Schemes

Carsten Carstensen and Friederike Hellwig
SIAM Journal on Numerical Analysis 56 (2) 1091 (2018)
https://doi.org/10.1137/17M1146671

Discrete least-squares finite element methods

Brendan Keith, Socratis Petrides, Federico Fuentes and Leszek Demkowicz
Computer Methods in Applied Mechanics and Engineering 327 226 (2017)
https://doi.org/10.1016/j.cma.2017.08.043

A Local Meshless Method for Steady State Convection Dominated Flows

Siraj-ul-Islam and Vikendra Singh
International Journal of Computational Methods 14 (06) 1750067 (2017)
https://doi.org/10.1142/S0219876217500670

Using a DPG method to validate DMA experimental calibration of viscoelastic materials

Federico Fuentes, Leszek Demkowicz and Aleta Wilder
Computer Methods in Applied Mechanics and Engineering 325 748 (2017)
https://doi.org/10.1016/j.cma.2017.07.012

Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

Truman Ellis, Jesse Chan and Leszek Demkowicz
Lecture Notes in Computational Science and Engineering, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations 114 179 (2016)
https://doi.org/10.1007/978-3-319-41640-3_6

Breaking spaces and forms for the DPG method and applications including Maxwell equations

C. Carstensen, L. Demkowicz and J. Gopalakrishnan
Computers & Mathematics with Applications 72 (3) 494 (2016)
https://doi.org/10.1016/j.camwa.2016.05.004

Towards adaptive discontinuous Petrov‐Galerkin methods

P. Bringmann, C. Carstensen, D. Gallistl, F. Hellwig, D. Peterseim, S. Puttkammer, H. Rabus and J. Storn
PAMM 16 (1) 741 (2016)
https://doi.org/10.1002/pamm.201610359

The DPG methodology applied to different variational formulations of linear elasticity

Brendan Keith, Federico Fuentes and Leszek Demkowicz
Computer Methods in Applied Mechanics and Engineering 309 579 (2016)
https://doi.org/10.1016/j.cma.2016.05.034

Interpolation of Inverse Operators for Preconditioning Parameter-Dependent Equations

Olivier Zahm and Anthony Nouy
SIAM Journal on Scientific Computing 38 (2) A1044 (2016)
https://doi.org/10.1137/15M1019210

A discontinuous Petrov–Galerkin methodology for adaptive solutions to the incompressible Navier–Stokes equations

Nathan V. Roberts, Leszek Demkowicz and Robert Moser
Journal of Computational Physics 301 456 (2015)
https://doi.org/10.1016/j.jcp.2015.07.014

A Robust Residual-Type a Posteriori Error Estimator for Convection–Diffusion Equations

Shaohong Du and Zhimin Zhang
Journal of Scientific Computing 65 (1) 138 (2015)
https://doi.org/10.1007/s10915-014-9972-4

Ideal minimal residual-based proper generalized decomposition for non-symmetric multi-field models – Application to transient elastodynamics in space-time domain

L. Boucinha, A. Ammar, A. Gravouil and A. Nouy
Computer Methods in Applied Mechanics and Engineering 273 56 (2014)
https://doi.org/10.1016/j.cma.2014.01.019

A robust DPG method for convection-dominated diffusion problems II: Adjoint boundary conditions and mesh-dependent test norms

Jesse Chan, Norbert Heuer, Tan Bui-Thanh and Leszek Demkowicz
Computers & Mathematics with Applications 67 (4) 771 (2014)
https://doi.org/10.1016/j.camwa.2013.06.010

Double greedy algorithms: Reduced basis methods for transport dominated problems

Wolfgang Dahmen, Christian Plesken and Gerrit Welper
ESAIM: Mathematical Modelling and Numerical Analysis 48 (3) 623 (2014)
https://doi.org/10.1051/m2an/2013103

A dual Petrov–Galerkin finite element method for the convection–diffusion equation

Jesse Chan, John A. Evans and Weifeng Qiu
Computers & Mathematics with Applications 68 (11) 1513 (2014)
https://doi.org/10.1016/j.camwa.2014.07.008

First order least squares method with weakly imposed boundary condition for convection dominated diffusion problems

Huangxin Chen, Guosheng Fu, Jingzhi Li and Weifeng Qiu
Computers & Mathematics with Applications 68 (12) 1635 (2014)
https://doi.org/10.1016/j.camwa.2014.11.001

A robust Petrov–Galerkin discretisation of convection–diffusion equations

Dirk Broersen and Rob Stevenson
Computers & Mathematics with Applications 68 (11) 1605 (2014)
https://doi.org/10.1016/j.camwa.2014.06.019

A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems

M. Billaud-Friess, A. Nouy and O. Zahm
ESAIM: Mathematical Modelling and Numerical Analysis 48 (6) 1777 (2014)
https://doi.org/10.1051/m2an/2014019

Robust DPG Method for Convection-Dominated Diffusion Problems

Leszek Demkowicz and Norbert Heuer
SIAM Journal on Numerical Analysis 51 (5) 2514 (2013)
https://doi.org/10.1137/120862065

Automatically stable discontinuous Petrov–Galerkin methods for stationary transport problems: Quasi-optimal test space norm

Antti H. Niemi, Nathaniel O. Collier and Victor M. Calo
Computers & Mathematics with Applications 66 (10) 2096 (2013)
https://doi.org/10.1016/j.camwa.2013.07.016

Adaptive Petrov--Galerkin Methods for First Order Transport Equations

Wolfgang Dahmen, Chunyan Huang, Christoph Schwab and Gerrit Welper
SIAM Journal on Numerical Analysis 50 (5) 2420 (2012)
https://doi.org/10.1137/110823158