{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,2]],"date-time":"2024-09-02T09:48:23Z","timestamp":1725270503695},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,10,6]],"date-time":"2016-10-06T00:00:00Z","timestamp":1475712000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003945","name":"Link\u00f6ping University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100003945","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2017,4]]},"DOI":"10.1007\/s10915-016-0303-9","type":"journal-article","created":{"date-parts":[[2016,10,6]],"date-time":"2016-10-06T05:56:38Z","timestamp":1475733398000},"page":"365-385","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":51,"title":["A Roadmap to Well Posed and Stable Problems in Computational Physics"],"prefix":"10.1007","volume":"71","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-7972-6183","authenticated-orcid":false,"given":"Jan","family":"Nordstr\u00f6m","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,10,6]]},"reference":[{"key":"303_CR1","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1137\/040604972","volume":"43","author":"J Nordstr\u00f6m","year":"2005","unstructured":"Nordstr\u00f6m, J., Sv\u00e4rd, M.: Well posed boundary conditions for the Navier\u2013Stokes equation. SIAM J. Numer. Anal. 43, 1231\u20131255 (2005)","journal-title":"SIAM J. Numer. Anal."},{"key":"303_CR2","volume-title":"Time Dependent Problems and Difference Methods","author":"B Gustafsson","year":"1995","unstructured":"Gustafsson, B., Kreiss, H.-O., Oliger, J.: Time Dependent Problems and Difference Methods. Wiley, New York (1995)"},{"key":"303_CR3","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1002\/cpa.3160230304","volume":"23","author":"H-O Kreiss","year":"1970","unstructured":"Kreiss, H.-O.: Initial boundary value problems for hyperbolic systems. Commun. Pure Appl. Math. 23, 277\u2013298 (1970)","journal-title":"Commun. Pure Appl. Math."},{"key":"303_CR4","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1002\/cpa.3160300606","volume":"30","author":"JC Strikwerda","year":"1977","unstructured":"Strikwerda, J.C.: Initial boundary value problems for incompletely parabolic systems. Commun. Pure Appl. Math. 30, 797\u2013822 (1977)","journal-title":"Commun. Pure Appl. Math."},{"key":"303_CR5","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/S0168-9274(98)00025-7","volume":"27","author":"SV Tsynkov","year":"1998","unstructured":"Tsynkov, S.V.: Numerical solution of problems on unbounded domains. A review. Appl. Numer. Math. 27, 465\u2013532 (1998)","journal-title":"Appl. Numer. Math."},{"key":"303_CR6","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.wavemoti.2003.12.004","volume":"39","author":"D Givoli","year":"2004","unstructured":"Givoli, D.: High-order local non-reflecting boundary conditions: a review. Wave Motion 39, 319\u2013326 (2004)","journal-title":"Wave Motion"},{"key":"303_CR7","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1006\/jcph.1998.6114","volume":"148","author":"MH Carpenter","year":"1999","unstructured":"Carpenter, M.H., Nordstr\u00f6m, J., Gottlieb, D.: A stable and conservative interface treatment of arbitrary spatial accuracy. J. Comput. Phys. 148, 341\u2013365 (1999)","journal-title":"J. Comput. Phys."},{"key":"303_CR8","doi-asserted-by":"crossref","first-page":"1020","DOI":"10.1016\/j.jcp.2007.01.023","volume":"225","author":"M Sv\u00e4rd","year":"2007","unstructured":"Sv\u00e4rd, M., Carpenter, M.H., Nordstr\u00f6m, J.: A stable high-order finite difference scheme for the compressible Navier\u2013Stokes equations, far-field boundary conditions. J. Comput. Phys. 225, 1020\u20131038 (2007)","journal-title":"J. Comput. Phys."},{"key":"303_CR9","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/S0168-9274(02)00239-8","volume":"48","author":"J Nordstr\u00f6m","year":"2003","unstructured":"Nordstr\u00f6m, J., Forsberg, K., Adamsson, C., Eliasson, P.: Finite volume methods, unstructured meshes and strict stability. Appl. Numer. Math. 48, 453\u2013473 (2003)","journal-title":"Appl. Numer. Math."},{"key":"303_CR10","doi-asserted-by":"crossref","first-page":"4867","DOI":"10.1016\/j.jcp.2012.04.007","volume":"231","author":"J Nordstr\u00f6m","year":"2012","unstructured":"Nordstr\u00f6m, J., Eriksson, S., Eliasson, P.: Weak and strong wall boundary procedures and convergence to steady-state of the Navier\u2013Stokes equations. J. Comput. Phys. 231, 4867\u20134884 (2012)","journal-title":"J. Comput. Phys."},{"key":"303_CR11","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1006\/jcph.1996.0234","volume":"129","author":"MH Carpenter","year":"1996","unstructured":"Carpenter, M.H., Gottlieb, D.: Spectral methods on arbitrary grids. J. Comput. Phys. 129, 74\u201386 (1996)","journal-title":"J. Comput. Phys."},{"key":"303_CR12","doi-asserted-by":"crossref","first-page":"B835","DOI":"10.1137\/130932193","volume":"36","author":"MH Carpenter","year":"2014","unstructured":"Carpenter, M.H., Fisher, T.C., Nielsen, E.J., Frankel, S.H.: Entropy stable spectral collocation schemes for the Navier\u2013Stokes equations: discontinuous interfaces. SIAM J. Sci. Comput. 36, B835\u2013B867 (2014)","journal-title":"SIAM J. Sci. Comput."},{"key":"303_CR13","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1137\/S1064827594268488","volume":"17","author":"JS Hesthaven","year":"1996","unstructured":"Hesthaven, J.S., Gottlieb, D.: A stable penalty method for the compressible Navier\u2013Stokes equations: I. Open boundary conditions. SIAM J. Sci. Comput. 17, 579\u2013612 (1996)","journal-title":"SIAM J. Sci. Comput."},{"key":"303_CR14","doi-asserted-by":"crossref","first-page":"A1233","DOI":"10.1137\/120890144","volume":"35","author":"GJ Gassner","year":"2013","unstructured":"Gassner, G.J.: A skew-symmetric discontinuous Galerkin spectral element discretization and its relation to sbp-sat finite difference methods. SIAM J. Sci. Comput. 35, A1233\u2013A1253 (2013)","journal-title":"SIAM J. Sci. Comput."},{"key":"303_CR15","doi-asserted-by":"crossref","unstructured":"Huynh, H.: A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods. In: 18th AIAA computational fluid dynamics conference, Miami, FL, 25\u201328 June 2007","DOI":"10.2514\/6.2007-4079"},{"key":"303_CR16","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1016\/j.cma.2013.08.012","volume":"267","author":"P Castonguay","year":"2013","unstructured":"Castonguay, P., Williams, D.M., Vincent, P.E., Jameson, A.J.: Energy stable flux reconstruction schemes for advection\u2013diffusion problems. Comput. Methods Appl. Mech. Eng. 267, 400\u2013417 (2013)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"303_CR17","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1142\/S0219891606000896","volume":"3","author":"E Tadmor","year":"2006","unstructured":"Tadmor, E., Zhong, W.: Entropy stable approximations of Navier\u2013Stokes equations with no aritificial numerical viscosity. J. Hyperbolic Differ. Equ. 3(3), 529\u2013559 (2006)","journal-title":"J. Hyperbolic Differ. Equ."},{"issue":"1","key":"303_CR18","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.jcp.2015.03.026","volume":"292","author":"M Parsani","year":"2015","unstructured":"Parsani, M., Carpenter, M.H., Nielsen, E.J.: Entropy stable wall boundary conditions for the three-dimensional compressible Navier\u2013Stokes equations. J. Comput. Phys. 292(1), 88\u2013113 (2015)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"303_CR19","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1007\/s10915-012-9624-5","volume":"55","author":"JE Kozdon","year":"2013","unstructured":"Kozdon, J.E., Dunham, E.M., Nordstr\u00f6m, J.: Simulation of dynamic earthquake ruptures in complex geometries using high-order finite difference methods. J. Sci. Comput. 55(1), 92\u2013124 (2013)","journal-title":"J. Sci. Comput."},{"key":"303_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0021-9991(81)90077-2","volume":"41","author":"S Abarbanel","year":"1981","unstructured":"Abarbanel, S., Gottlieb, D.: Optimal time splitting for two- and three-dimensional Navier\u2013Stokes equations with mixed derivatives. J. Comput. Phys. 41, 1\u201333 (1981)","journal-title":"J. Comput. Phys."},{"key":"303_CR21","volume-title":"High Order Difference Methods for Time-Dependent PDE. Springer Series in Computational Mathematics","author":"B Gustafsson","year":"2008","unstructured":"Gustafsson, B.: High Order Difference Methods for Time-Dependent PDE. Springer Series in Computational Mathematics. Springer, Berlin (2008)"},{"key":"303_CR22","doi-asserted-by":"crossref","first-page":"1738","DOI":"10.1016\/j.jcp.2014.02.031","volume":"268","author":"M Sv\u00e4rd","year":"2014","unstructured":"Sv\u00e4rd, M., Nordstr\u00f6m, J.: Review of summation-by-parts schemes for initial\u2013boundary-value problems. J. Comput. Phys. 268, 1738 (2014)","journal-title":"J. Comput. Phys."},{"key":"303_CR23","volume-title":"Initial Boundary Value Problems and the Navier\u2013Stokes Equations","author":"HO Kreiss","year":"1989","unstructured":"Kreiss, H.O., Lorenz, J.: Initial Boundary Value Problems and the Navier\u2013Stokes Equations. Academic Press, Boston (1989)"},{"key":"303_CR24","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/BF01386051","volume":"6","author":"G Strang","year":"1964","unstructured":"Strang, G.: Accurate partial difference methods II: non-linear problems. Numer. Math. 6, 37\u201346 (1964)","journal-title":"Numer. Math."},{"key":"303_CR25","unstructured":"Sudirham, J.J., van der Vegt, J.J.W., van Damme, R.M.J.: A study on discontinuous Galerkin finite element methods for eliptic problems, Memorandum 1690. University of Twente, Faculty of EEMCS (2003)"},{"key":"303_CR26","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1137\/S0036142901384162","volume":"39","author":"DN Arnold","year":"2001","unstructured":"Arnold, D.N., Brezzi, F., Cockburn, B., Marini, L.D.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749\u20131779 (2001)","journal-title":"SIAM J. Numer. Anal."},{"key":"303_CR27","doi-asserted-by":"crossref","first-page":"593609","DOI":"10.1017\/jfm.2012.351","volume":"709","author":"J Nordstr\u00f6m","year":"2012","unstructured":"Nordstr\u00f6m, J., L\u00f6nn, B.: Energy decay of vortices in viscous fluids: an applied mathematics view. J. Fluid Mech. 709, 593609 (2012)","journal-title":"J. Fluid Mech."},{"issue":"1","key":"303_CR28","doi-asserted-by":"crossref","first-page":"874","DOI":"10.1016\/j.jcp.2007.01.010","volume":"225","author":"J Nordstr\u00f6m","year":"2007","unstructured":"Nordstr\u00f6m, J., Mattsson, K., Swanson, Charles: Boundary conditions for a divergence free velocity\u2013pressure formulation of the Navier\u2013Stokes equations. J. Comput. Phys. 225(1), 874\u2013890 (2007)","journal-title":"J. Comput. Phys."},{"key":"303_CR29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jcp.2014.10.061","volume":"82","author":"J Nordstr\u00f6m","year":"2015","unstructured":"Nordstr\u00f6m, J., Wahlsten, M.: Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations. J. Comput. Phys. 82, 1\u201322 (2015)","journal-title":"J. Comput. Phys."},{"key":"303_CR30","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511840371","volume-title":"Topics in Matrix Analysis","author":"RA Horn","year":"1991","unstructured":"Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1991)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0303-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-016-0303-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0303-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,24]],"date-time":"2017-06-24T20:29:04Z","timestamp":1498336144000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-016-0303-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,6]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,4]]}},"alternative-id":["303"],"URL":"https:\/\/doi.org\/10.1007\/s10915-016-0303-9","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,10,6]]}}}