{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,16]],"date-time":"2024-09-16T05:23:29Z","timestamp":1726464209587},"reference-count":51,"publisher":"Elsevier BV","issue":"10","license":[{"start":{"date-parts":[[2013,12,1]],"date-time":"2013-12-01T00:00:00Z","timestamp":1385856000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2017,12,2]],"date-time":"2017-12-02T00:00:00Z","timestamp":1512172800000},"content-version":"vor","delay-in-days":1462,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computers & Mathematics with Applications"],"published-print":{"date-parts":[[2013,12]]},"DOI":"10.1016\/j.camwa.2013.07.016","type":"journal-article","created":{"date-parts":[[2013,9,24]],"date-time":"2013-09-24T10:03:48Z","timestamp":1380017028000},"page":"2096-2113","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":20,"title":["Automatically stable discontinuous Petrov\u2013Galerkin methods for stationary transport problems: Quasi-optimal test space norm"],"prefix":"10.1016","volume":"66","author":[{"given":"Antti H.","family":"Niemi","sequence":"first","affiliation":[]},{"given":"Nathaniel O.","family":"Collier","sequence":"additional","affiliation":[]},{"given":"Victor M.","family":"Calo","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.camwa.2013.07.016_br000005","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1002\/nme.1620110113","article-title":"An \u2018upwind\u2019 finite element scheme for two-dimensional convective transport equation","volume":"11","author":"Heinrich","year":"1977","journal-title":"International Journal for Numerical Methods in Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000010","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0045-7825(82)90071-8","article-title":"Streamline upwind\/Petrov\u2013Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier\u2013Stokes equation","volume":"32","author":"Brooks","year":"1982","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000015","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/0045-7825(92)90114-Y","article-title":"A new approach to algorithms for convection problems which are based on exact transport + projection","volume":"100","author":"Johnson","year":"1992","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000020","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/0021-9991(86)90121-X","article-title":"An adaptive characteristic Petrov\u2013Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable","volume":"67","author":"Demkowicz","year":"1986","journal-title":"Journal of Computational Physics"},{"key":"10.1016\/j.camwa.2013.07.016_br000025","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/0045-7825(86)90086-1","article-title":"An adaptive characteristic Petrov\u2013Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in two space variables","volume":"55","author":"Demkowicz","year":"1986","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"1","key":"10.1016\/j.camwa.2013.07.016_br000030","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1006\/jcph.1993.1057","article-title":"Non-oscillatory and non-diffusive solution of convection problems by the iteratively reweighted least-squares finite element method","volume":"105","author":"Jiang","year":"1993","journal-title":"Journal of Computational Physics"},{"issue":"6","key":"10.1016\/j.camwa.2013.07.016_br000035","doi-asserted-by":"crossref","first-page":"1293","DOI":"10.1051\/m2an:1999145","article-title":"Stabilization of Galerkin approximations of transport equations by subgrid modeling","volume":"33","author":"Guermond","year":"1999","journal-title":"Mathematical Modelling and Numerical Analysis"},{"key":"10.1016\/j.camwa.2013.07.016_br000040","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/S0045-7825(96)01221-2","article-title":"b=\u222bg","volume":"145","author":"Brezzi","year":"1997","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000045","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/S0045-7825(97)00206-5","article-title":"Comparison of some finite element methods for solving the diffusion\u2013convection\u2013reaction equation","volume":"156","author":"Codina","year":"1998","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000050","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/S0045-7825(97)00119-9","article-title":"Derivation of stabilized equations for numerical solution of advective-diffusive transport and fluid flow problems","volume":"151","author":"O\u00f1ate","year":"1998","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"13\u201314","key":"10.1016\/j.camwa.2013.07.016_br000055","doi-asserted-by":"crossref","first-page":"1601","DOI":"10.1016\/S0045-7825(00)00179-1","article-title":"Modeling subgrid viscosity for advection\u2013diffusion problems","volume":"190","author":"Brezzi","year":"2000","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"2","key":"10.1016\/j.camwa.2013.07.016_br000060","doi-asserted-by":"crossref","first-page":"714","DOI":"10.1137\/S0036142902417054","article-title":"A finite element technique for solving first-order PDEs in Lp","volume":"42","author":"Guermond","year":"2004","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"10.1016\/j.camwa.2013.07.016_br000065","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.1137\/050640382","article-title":"Analysis of a multiscale discontinuous Galerkin method for convection diffusion problems","volume":"44","author":"Buffa","year":"2006","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"10.1016\/j.camwa.2013.07.016_br000070","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.cma.2009.09.019","article-title":"Enforcement of constraints and maximum principles in the variational multiscale method","volume":"199","author":"Hughes","year":"2009","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000075","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/0045-7825(84)90158-0","article-title":"Finite element methods for linear hyperbolic problems","volume":"45","author":"Johnson","year":"1984","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000080","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1016\/j.cma.2005.05.028","article-title":"Revisiting stabilized finite element methods for the advective-diffusive equation","volume":"195","author":"Franca","year":"2006","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"year":"1993","series-title":"A finite element formulation for the numerical solution of the convection\u2013diffusion equation, Tech. Rep. 14","author":"Codina","key":"10.1016\/j.camwa.2013.07.016_br000085"},{"key":"10.1016\/j.camwa.2013.07.016_br000090","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/0045-7825(92)90143-8","article-title":"Stabilized finite element methods, I. Application to the advective-diffusive model","volume":"95","author":"Franca","year":"1992","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000095","doi-asserted-by":"crossref","first-page":"4135","DOI":"10.1016\/j.cma.2004.10.008","article-title":"Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement","volume":"194","author":"Hughes","year":"2005","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000100","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.cma.2009.02.036","article-title":"Isogeometric analysis using T-splines","volume":"199","author":"Bazilevs","year":"2010","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000105","doi-asserted-by":"crossref","first-page":"1558","DOI":"10.1016\/j.cma.2010.01.003","article-title":"A class of discontinuous Petrov\u2013Galerkin methods, part I: the transport equation","volume":"199","author":"Demkowicz","year":"2009","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000110","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1002\/num.20640","article-title":"A class of discontinuous Petrov\u2013Galerkin methods, part II: optimal test functions","volume":"27","author":"Demkowicz","year":"2010","journal-title":"Numerical Methods for Partial Differential Equations"},{"key":"10.1016\/j.camwa.2013.07.016_br000115","first-page":"12","article-title":"A new paradigm for discretizing difficult problems: discontinuous Petrov\u2013Galerkin method with optimal test functions","volume":"28","author":"Demkowicz","year":"2011","journal-title":"IACM Expressions"},{"key":"10.1016\/j.camwa.2013.07.016_br000120","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/0045-7825(84)90152-X","article-title":"Approximate symmetrization and Petrov\u2013Galerkin methods for diffusion\u2013convection problems","volume":"45","author":"Barrett","year":"1984","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000125","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/0045-7825(87)90167-8","article-title":"Petrov\u2013Galerkin formulations of the Timoshenko beam problem","volume":"63","author":"Loula","year":"1987","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000130","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/BF01395881","article-title":"A new family of stable elements for nearly incompressible elasticity based on a mixed Petrov\u2013Galerkin finite element formulation","volume":"53","author":"Franca","year":"1988","journal-title":"Numerische Mathematik"},{"key":"10.1016\/j.camwa.2013.07.016_br000135","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/0045-7825(87)90074-0","article-title":"Stability, convergence and accuracy of new finite element method for the circular arch problem","volume":"63","author":"Loula","year":"1987","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000140","doi-asserted-by":"crossref","first-page":"3391","DOI":"10.1016\/S0045-7825(02)00254-2","article-title":"The discontinuous Petrov\u2013Galerkin method for elliptic problems","volume":"191","author":"Bottasso","year":"2002","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000145","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1016\/j.apnum.2011.09.002","article-title":"A class of discontinuous Petrov\u2013Galerkin methods, part III: adaptivity","volume":"62","author":"Demkowicz","year":"2012","journal-title":"Applied Numerical Mathematics"},{"issue":"9\u201312","key":"10.1016\/j.camwa.2013.07.016_br000150","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1016\/j.cma.2010.10.018","article-title":"Discontinuous Petrov\u2013Galerkin method with optimal test functions for thin-body problems in solid mechanics","volume":"200","author":"Niemi","year":"2011","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"10.1016\/j.camwa.2013.07.016_br000155","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1051\/m2an\/2012003","article-title":"Adaptivity and variational stabilization for convection\u2013diffusion equations","volume":"46","author":"Cohen","year":"2012","journal-title":"ESAIM: Mathematical Modelling and Numerical Analysis"},{"key":"10.1016\/j.camwa.2013.07.016_br000160","doi-asserted-by":"crossref","first-page":"2420","DOI":"10.1137\/110823158","article-title":"Adaptive Petrov\u2013Galerkin methods for first order transport equations","volume":"50","author":"Dahmen","year":"2012","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"10.1016\/j.camwa.2013.07.016_br000165","unstructured":"W. Dahmen, C. Plesken, G. Welper, Double greedy algorithms: reduced basis methods for transport dominated problems, IGPM-Preprint."},{"year":"2007","series-title":"Computing with hp-Adaptive Finite Elements: Volume 1 One and Two Dimensional Elliptic and Maxwell Problems","author":"Demkowicz","key":"10.1016\/j.camwa.2013.07.016_br000170"},{"key":"10.1016\/j.camwa.2013.07.016_br000175","doi-asserted-by":"crossref","first-page":"1862","DOI":"10.1016\/j.procs.2011.04.202","article-title":"Discontinuous Petrov\u2013Galerkin method based on the optimal test space norm for one-dimensional transport problems","volume":"4","author":"Niemi","year":"2011","journal-title":"Procedia Computer Science"},{"key":"10.1016\/j.camwa.2013.07.016_br000180","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.jocs.2011.07.003","article-title":"Discontinuous Petrov\u2013Galerkin method based on the optimal test space norm for steady transport problems in one space dimension","volume":"4","author":"Niemi","year":"2013","journal-title":"Journal of Computational Science"},{"key":"10.1016\/j.camwa.2013.07.016_br000185","series-title":"Encyclopedia of Computational Mechanics","first-page":"59","article-title":"Multiscale and stabilized methods","volume":"vol. 3","author":"Hughes","year":"2007"},{"key":"10.1016\/j.camwa.2013.07.016_br000190","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1007\/BF02165003","article-title":"Error-bounds for finite element method","volume":"16","author":"Babu\u0161ka","year":"1971","journal-title":"Numerische Mathematik"},{"key":"10.1016\/j.camwa.2013.07.016_br000195","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1051\/m2an\/197408R201291","article-title":"On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers","volume":"8","author":"Brezzi","year":"1974","journal-title":"RAIRO Analyse Num\u00e9rique"},{"year":"2006","series-title":"Babu\u0161ka \u21d4 Brezzi, ICES REPORT 06-08","author":"Demkowicz","key":"10.1016\/j.camwa.2013.07.016_br000200"},{"key":"10.1016\/j.camwa.2013.07.016_br000205","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1137\/0729075","article-title":"On locking and robustness of the finite element method","volume":"29","author":"Babu\u0161ka","year":"1992","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"10.1016\/j.camwa.2013.07.016_br000210","doi-asserted-by":"crossref","first-page":"2406","DOI":"10.1016\/j.jcp.2010.12.001","article-title":"A class of discontinuous Petrov\u2013Galerkin methods, part IV: the optimal test norm and time-harmonic wave propagation in 1D","volume":"230","author":"Zitelli","year":"2011","journal-title":"Journal of Computational Physics"},{"issue":"5","key":"10.1016\/j.camwa.2013.07.016_br000215","doi-asserted-by":"crossref","first-page":"1788","DOI":"10.1137\/100809799","article-title":"Analysis of the DPG method for the Poisson equation","volume":"49","author":"Demkowicz","year":"2011","journal-title":"SIAM Journal on Numerical Analysis"},{"year":"2011","series-title":"Robust DPG method for convection-dominated diffusion problems, ICES REPORT 11-33","author":"Demkowicz","key":"10.1016\/j.camwa.2013.07.016_br000220"},{"year":"2010","series-title":"Layer-Adapted Meshes for Reaction\u2013Convection\u2013Diffusion Problems","author":"Lin\u00df","key":"10.1016\/j.camwa.2013.07.016_br000225"},{"issue":"5","key":"10.1016\/j.camwa.2013.07.016_br000230","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1515\/rnam.1989.4.5.397","article-title":"Grid approximation of singularly perturbed boundary value problems with a regular boundary layer","volume":"4","author":"Shishkin","year":"1989","journal-title":"Russian Journal of Numerical Analysis and Mathematical Modelling"},{"key":"10.1016\/j.camwa.2013.07.016_br000235","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.1090\/S0025-5718-96-00781-8","article-title":"The p and hp versions of the finite element method for problems with boundary layers","volume":"65","author":"Schwab","year":"1996","journal-title":"Mathematics of Computation"},{"key":"10.1016\/j.camwa.2013.07.016_br000240","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1142\/S0218202598000135","article-title":"The hp finite element method for singularly perturbed problems in smooth domains","volume":"8","author":"Xenophontos","year":"1998","journal-title":"Mathematical Models and Methods in Applied Sciences (M3AS)"},{"issue":"4","key":"10.1016\/j.camwa.2013.07.016_br000245","doi-asserted-by":"crossref","first-page":"1520","DOI":"10.1137\/S0036142997317602","article-title":"hp FEM for reaction\u2013diffusion equations I: robust exponential convergence","volume":"35","author":"Melenk","year":"1998","journal-title":"SIAM Journal on Numerical Analysis"},{"year":"1987","series-title":"The Finite Element Method: Linear Static and Dynamic Finite Element Analysis","author":"Hughes","key":"10.1016\/j.camwa.2013.07.016_br000250"},{"key":"10.1016\/j.camwa.2013.07.016_br000255","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1090\/S0025-5718-1993-1149289-9","article-title":"Adaptive streamline diffusion finite element methods for stationary convection\u2013diffusion problems","volume":"60","author":"Eriksson","year":"1993","journal-title":"Mathematics of Computation"}],"container-title":["Computers & Mathematics with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0898122113004446?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0898122113004446?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,10,12]],"date-time":"2018-10-12T15:20:34Z","timestamp":1539357634000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0898122113004446"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12]]},"references-count":51,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["S0898122113004446"],"URL":"https:\/\/doi.org\/10.1016\/j.camwa.2013.07.016","relation":{},"ISSN":["0898-1221"],"issn-type":[{"type":"print","value":"0898-1221"}],"subject":[],"published":{"date-parts":[[2013,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Automatically stable discontinuous Petrov\u2013Galerkin methods for stationary transport problems: Quasi-optimal test space norm","name":"articletitle","label":"Article Title"},{"value":"Computers & Mathematics with Applications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.camwa.2013.07.016","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2013 Elsevier Ltd. All rights reserved.","name":"copyright","label":"Copyright"}]}}