Kopriva, David A.; Gassner, Gregor J. A split-form, stable CG/DG-SEM for wave propagation modeled by linear hyperbolic systems. (English) Zbl 1500.65084 J. Sci. Comput. 89, No. 1, Paper No. 2, 29 p. (2021). MSC: 65M70 65M60 65L06 65N35 65N30 65N50 35L65 35L02 76Q05 PDFBibTeX XMLCite \textit{D. A. Kopriva} and \textit{G. J. Gassner}, J. Sci. Comput. 89, No. 1, Paper No. 2, 29 p. (2021; Zbl 1500.65084) Full Text: DOI arXiv
Kopriva, David A.; Gassner, Gregor J.; Nordström, Jan Stability of discontinuous Galerkin spectral element schemes for wave propagation when the coefficient matrices have jumps. (English) Zbl 1476.65317 J. Sci. Comput. 88, No. 1, Paper No. 3, 23 p. (2021). MSC: 65N35 65N30 65L06 35F05 PDFBibTeX XMLCite \textit{D. A. Kopriva} et al., J. Sci. Comput. 88, No. 1, Paper No. 3, 23 p. (2021; Zbl 1476.65317) Full Text: DOI arXiv
Hindenlang, Florian J.; Gassner, Gregor J.; Kopriva, David A. Stability of wall boundary condition procedures for discontinuous Galerkin spectral element approximations of the compressible Euler equations. (English) Zbl 1484.65256 Sherwin, Spencer J. (ed.) et al., Spectral and high order methods for partial differential equations, ICOSAHOM 2018. Selected papers from the ICOSAHOM conference, London, UK, July 9–13, 2018. Cham: Springer. Lect. Notes Comput. Sci. Eng. 134, 3-19 (2020). MSC: 65M70 65M06 65L06 65N35 65M60 65M12 65D32 76N10 76M22 35Q31 PDFBibTeX XMLCite \textit{F. J. Hindenlang} et al., Lect. Notes Comput. Sci. Eng. 134, 3--19 (2020; Zbl 1484.65256) Full Text: DOI arXiv
Kopriva, David A.; Hindenlang, Florian J.; Bolemann, Thomas; Gassner, Gregor J. Free-stream preservation for curved geometrically non-conforming discontinuous Galerkin spectral elements. (English) Zbl 1448.76111 J. Sci. Comput. 79, No. 3, 1389-1408 (2019). MSC: 76M22 65M60 65M70 PDFBibTeX XMLCite \textit{D. A. Kopriva} et al., J. Sci. Comput. 79, No. 3, 1389--1408 (2019; Zbl 1448.76111) Full Text: DOI arXiv
Gassner, Gregor J.; Winters, Andrew R.; Hindenlang, Florian J.; Kopriva, David A. Correction to: “The BR1 scheme is stable for the compressible Navier-Stokes equations”. (English) Zbl 1466.65131 J. Sci. Comput. 77, No. 1, 201-203 (2018). MSC: 65M60 65M70 65M12 76N10 35Q35 76M22 PDFBibTeX XMLCite \textit{G. J. Gassner} et al., J. Sci. Comput. 77, No. 1, 201--203 (2018; Zbl 1466.65131) Full Text: DOI
Gassner, Gregor J.; Winters, Andrew R.; Hindenlang, Florian J.; Kopriva, David A. The BR1 scheme is stable for the compressible Navier-Stokes equations. (English) Zbl 1407.65189 J. Sci. Comput. 77, No. 1, 154-200 (2018); correction ibid. 77, No. 1, 201-203 (2018). MSC: 65M60 65M70 65M12 76N10 35Q35 76M22 PDFBibTeX XMLCite \textit{G. J. Gassner} et al., J. Sci. Comput. 77, No. 1, 154--200 (2018; Zbl 1407.65189) Full Text: DOI arXiv
Kopriva, David A. Stability of overintegration methods for nodal discontinuous Galerkin spectral element methods. (English) Zbl 1404.65174 J. Sci. Comput. 76, No. 1, 426-442 (2018). MSC: 65M60 65M70 65R32 PDFBibTeX XMLCite \textit{D. A. Kopriva}, J. Sci. Comput. 76, No. 1, 426--442 (2018; Zbl 1404.65174) Full Text: DOI arXiv
Manzanero, Juan; Rubio, Gonzalo; Ferrer, Esteban; Valero, Eusebio; Kopriva, David A. Insights on aliasing driven instabilities for advection equations with application to Gauss-Lobatto discontinuous Galerkin methods. (English) Zbl 1422.65263 J. Sci. Comput. 75, No. 3, 1262-1281 (2018). MSC: 65M60 65M70 65D30 65M12 35L65 35Q35 PDFBibTeX XMLCite \textit{J. Manzanero} et al., J. Sci. Comput. 75, No. 3, 1262--1281 (2018; Zbl 1422.65263) Full Text: DOI arXiv
Kopriva, David A. A polynomial spectral calculus for analysis of DG spectral element methods. (English) Zbl 1382.65345 Bittencourt, Marco L. (ed.) et al., Spectral and high order methods for partial differential equations, ICOSAHOM 2016. Selected papers from the ICOSAHOM conference, June 27 – July 1, 2016, Rio de Janeiro, Brazil. Cham: Springer (ISBN 978-3-319-65869-8/hbk; 978-3-319-65870-4/ebook). Lecture Notes in Computational Science and Engineering 119, 21-40 (2017). MSC: 65M70 35L04 PDFBibTeX XMLCite \textit{D. A. Kopriva}, Lect. Notes Comput. Sci. Eng. 119, 21--40 (2017; Zbl 1382.65345) Full Text: DOI arXiv
Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A. An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry. (English) Zbl 1380.65291 J. Comput. Phys. 340, 200-242 (2017). MSC: 65M60 35Q35 65M70 PDFBibTeX XMLCite \textit{N. Wintermeyer} et al., J. Comput. Phys. 340, 200--242 (2017; Zbl 1380.65291) Full Text: DOI arXiv
Kopriva, David A.; Nordström, Jan; Gassner, Gregor J. Error boundedness of discontinuous Galerkin spectral element approximations of hyperbolic problems. (English) Zbl 1371.65097 J. Sci. Comput. 72, No. 1, 314-330 (2017). MSC: 65M15 35L04 65M60 65M70 PDFBibTeX XMLCite \textit{D. A. Kopriva} et al., J. Sci. Comput. 72, No. 1, 314--330 (2017; Zbl 1371.65097) Full Text: DOI Link
Gassner, Gregor J.; Winters, Andrew R.; Kopriva, David A. A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations. (English) Zbl 1410.65393 Appl. Math. Comput. 272, Part 2, 291-308 (2016). MSC: 65M70 65M60 76B15 PDFBibTeX XMLCite \textit{G. J. Gassner} et al., Appl. Math. Comput. 272, Part 2, 291--308 (2016; Zbl 1410.65393) Full Text: DOI Link
Kopriva, David A.; Winters, Andrew R.; Bohm, Marvin; Gassner, Gregor J. A provably stable discontinuous Galerkin spectral element approximation for moving hexahedral meshes. (English) Zbl 1390.76653 Comput. Fluids 139, 148-160 (2016). MSC: 76M22 76M10 65M70 65M12 65M60 PDFBibTeX XMLCite \textit{D. A. Kopriva} et al., Comput. Fluids 139, 148--160 (2016; Zbl 1390.76653) Full Text: DOI arXiv
Gassner, Gregor J.; Winters, Andrew R.; Kopriva, David A. Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations. (English) Zbl 1422.65280 J. Comput. Phys. 327, 39-66 (2016). MSC: 65M70 65M60 76D05 35Q31 PDFBibTeX XMLCite \textit{G. J. Gassner} et al., J. Comput. Phys. 327, 39--66 (2016; Zbl 1422.65280) Full Text: DOI arXiv
Winters, Andrew R.; Kopriva, David A. Efficient and high order explicit local time stepping on moving DG spectral element meshes. (English) Zbl 1352.65275 Kirby, Robert M. (ed.) et al., Spectral and high order methods for partial differential equations, ICOSAHOM 2014. Selected papers from the ICOSAHOM conference, June 23–27, 2014, Salt Lake City, UT, USA. Cham: Springer (ISBN 978-3-319-19799-9/hbk; 978-3-319-19800-2/ebook). Lecture Notes in Computational Science and Engineering 106, 513-522 (2015). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 65M06 65M60 65M70 65Y05 65M50 PDFBibTeX XMLCite \textit{A. R. Winters} and \textit{D. A. Kopriva}, Lect. Notes Comput. Sci. Eng. 106, 513--522 (2015; Zbl 1352.65275) Full Text: DOI
Rubio, Gonzalo; Fraysse, François; Kopriva, David A.; Valero, Eusebio Quasi-a priori truncation error estimation in the DGSEM. (English) Zbl 1325.65138 J. Sci. Comput. 64, No. 2, 425-455 (2015). MSC: 65M60 65M70 65M15 65M12 35L65 PDFBibTeX XMLCite \textit{G. Rubio} et al., J. Sci. Comput. 64, No. 2, 425--455 (2015; Zbl 1325.65138) Full Text: DOI Link
Winters, Andrew R.; Kopriva, David A. ALE-DGSEM approximation of wave reflection and transmission from a moving medium. (English) Zbl 1349.65494 J. Comput. Phys. 263, 233-267 (2014). MSC: 65M60 65M12 76Q05 78A40 78M22 PDFBibTeX XMLCite \textit{A. R. Winters} and \textit{D. A. Kopriva}, J. Comput. Phys. 263, 233--267 (2014; Zbl 1349.65494) Full Text: DOI
Kopriva, David A.; Gassner, Gregor J. An energy stable discontinuous Galerkin spectral element discretization for variable coefficient advection problems. (English) Zbl 1303.65086 SIAM J. Sci. Comput. 36, No. 4, A2076-A2099 (2014). MSC: 65M70 65M60 35L65 65M12 PDFBibTeX XMLCite \textit{D. A. Kopriva} and \textit{G. J. Gassner}, SIAM J. Sci. Comput. 36, No. 4, A2076--A2099 (2014; Zbl 1303.65086) Full Text: DOI
Winters, Andrew R.; Kopriva, David A. High-order local time stepping on moving DG spectral element meshes. (English) Zbl 1286.65128 J. Sci. Comput. 58, No. 1, 176-202 (2014). MSC: 65M60 35L65 65M70 PDFBibTeX XMLCite \textit{A. R. Winters} and \textit{D. A. Kopriva}, J. Sci. Comput. 58, No. 1, 176--202 (2014; Zbl 1286.65128) Full Text: DOI Link
Garreau, Pierre; Kopriva, David A spectral element framework for option pricing under general exponential Lévy processes. (English) Zbl 1281.91182 J. Sci. Comput. 57, No. 2, 390-413 (2013). MSC: 91G60 65M70 91G20 60G51 60H15 PDFBibTeX XMLCite \textit{P. Garreau} and \textit{D. Kopriva}, J. Sci. Comput. 57, No. 2, 390--413 (2013; Zbl 1281.91182) Full Text: DOI
Kopriva, David A.; Jimenez, Edwin An assessment of the efficiency of nodal discontinuous Galerkin spectral element methods. (English) Zbl 1382.65346 Ansorge, Rainer (ed.) et al., Recent developments in the numerics of nonlinear hyperbolic conservation laws. Lectures presented at a workshop at the Mathematical Research Institute Oberwolfach, Germany, January 15–21, 2012. Berlin: Springer (ISBN 978-3-642-33220-3/hbk; 978-3-642-33221-0/ebook). Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM) 120, 223-235 (2013). MSC: 65M70 65M60 35L65 PDFBibTeX XMLCite \textit{D. A. Kopriva} and \textit{E. Jimenez}, in: Recent developments in the numerics of nonlinear hyperbolic conservation laws. Lectures presented at a workshop at the Mathematical Research Institute Oberwolfach, Germany, January 15--21, 2012. Berlin: Springer. 223--235 (2013; Zbl 1382.65346) Full Text: DOI
Namihira, Motoi; Kopriva, David A. Computation of the effects of uncertainty in volatility on option pricing and hedging. (English) Zbl 1255.91433 Int. J. Comput. Math. 89, No. 9, 1281-1302 (2012). MSC: 91G60 65C05 65N35 65N75 91G80 PDFBibTeX XMLCite \textit{M. Namihira} and \textit{D. A. Kopriva}, Int. J. Comput. Math. 89, No. 9, 1281--1302 (2012; Zbl 1255.91433) Full Text: DOI
Acosta Minoli, Cesar A.; Kopriva, David A. Boundary states at reflective moving boundaries. (English) Zbl 1250.78048 J. Comput. Phys. 231, No. 11, 4160-4184 (2012). MSC: 78M22 76Q05 65M70 35Q31 PDFBibTeX XMLCite \textit{C. A. Acosta Minoli} and \textit{D. A. Kopriva}, J. Comput. Phys. 231, No. 11, 4160--4184 (2012; Zbl 1250.78048) Full Text: DOI
Kopriva, David A.; Gassner, Gregor On the quadrature and weak form choices in collocation type discontinuous Galerkin spectral element methods. (English) Zbl 1203.65199 J. Sci. Comput. 44, No. 2, 136-155 (2010). MSC: 65M70 65M60 PDFBibTeX XMLCite \textit{D. A. Kopriva} and \textit{G. Gassner}, J. Sci. Comput. 44, No. 2, 136--155 (2010; Zbl 1203.65199) Full Text: DOI
Zhu, Wuming; Kopriva, David A. A spectral element approximation to price European options with one asset and stochastic volatility. (English) Zbl 1203.91307 J. Sci. Comput. 42, No. 3, 426-446 (2010). MSC: 91G60 65M60 65M70 91B70 91G20 PDFBibTeX XMLCite \textit{W. Zhu} and \textit{D. A. Kopriva}, J. Sci. Comput. 42, No. 3, 426--446 (2010; Zbl 1203.91307) Full Text: DOI
Zhu, Wuming; Kopriva, David A. A spectral element method to price European options. I. Single asset with and without jump diffusion. (English) Zbl 1203.91306 J. Sci. Comput. 39, No. 2, 222-243 (2009). MSC: 91G60 65M70 PDFBibTeX XMLCite \textit{W. Zhu} and \textit{D. A. Kopriva}, J. Sci. Comput. 39, No. 2, 222--243 (2009; Zbl 1203.91306) Full Text: DOI
Zhu, Wuming; Kopriva, David A. A spectral element approximation to price European options. II. the Black-Scholes model with two underlying assets. (English) Zbl 1203.91305 J. Sci. Comput. 39, No. 3, 323-339 (2009). MSC: 91G60 65M70 PDFBibTeX XMLCite \textit{W. Zhu} and \textit{D. A. Kopriva}, J. Sci. Comput. 39, No. 3, 323--339 (2009; Zbl 1203.91305) Full Text: DOI
Kopriva, David A. Implementing spectral methods for partial differential equations. Algorithms for scientists and engineers. (English) Zbl 1172.65001 Scientific Computation. Berlin: Springer (ISBN 978-90-481-2260-8/hbk; 978-90-481-2261-5/ebook). xviii, 394 p. (2009). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65-02 65N35 65M70 65Y15 65D32 35J25 35L15 65T60 PDFBibTeX XMLCite \textit{D. A. Kopriva}, Implementing spectral methods for partial differential equations. Algorithms for scientists and engineers. Berlin: Springer (2009; Zbl 1172.65001) Full Text: DOI
Kopriva, David A.; Woodruff, Stephen L.; Hussaini, M. Y. Discontinuous spectral element approximation of Maxwell’s equations. (English) Zbl 0957.78023 Cockburn, Bernardo (ed.) et al., Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24-26, 1999. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 11, 355-361 (2000). MSC: 78M10 78A25 PDFBibTeX XMLCite \textit{D. A. Kopriva} et al., Lect. Notes Comput. Sci. Eng. 11, 355--361 (2000; Zbl 0957.78023)
Kopriva, David A. Shock-fitted multidomain solution of supersonic flows. (English) Zbl 0924.76079 Comput. Methods Appl. Mech. Eng. 175, No. 3-4, 383-394 (1999). MSC: 76M25 76L05 76J20 65M70 PDFBibTeX XMLCite \textit{D. A. Kopriva}, Comput. Methods Appl. Mech. Eng. 175, No. 3--4, 383--394 (1999; Zbl 0924.76079) Full Text: DOI
Kopriva, David A. A staggered-grid multidomain spectral method for the compressible Navier-Stokes equations. (English) Zbl 0921.76121 J. Comput. Phys. 143, No. 1, 125-158 (1998). MSC: 76M25 76N10 65M70 PDFBibTeX XMLCite \textit{D. A. Kopriva}, J. Comput. Phys. 143, No. 1, 125--158 (1998; Zbl 0921.76121) Full Text: DOI
Kopriva, David A.; Kolias, John H. A conservative staggered-grid Chebyshev multidomain method for compressible flows. (English) Zbl 0847.76069 J. Comput. Phys. 125, No. 1, 244-261 (1996). MSC: 76M25 76N10 65M70 PDFBibTeX XMLCite \textit{D. A. Kopriva} and \textit{J. H. Kolias}, J. Comput. Phys. 125, No. 1, 244--261 (1996; Zbl 0847.76069) Full Text: DOI Link
Kopriva, David A. Spectral solution of the viscous blunt-body problem. II: Multidomain approximation. (English) Zbl 0913.76068 AIAA J. 34, No. 3, 560-564 (1996). MSC: 76M25 76J20 PDFBibTeX XMLCite \textit{D. A. Kopriva}, AIAA J. 34, No. 3, 560--564 (1996; Zbl 0913.76068) Full Text: DOI
Kopriva, David A. Multidomain spectral solution of compressible viscous flows. (English) Zbl 0822.76071 J. Comput. Phys. 115, No. 1, 184-199 (1994). Reviewer: V.Subba Rao (Madras) MSC: 76M25 76N10 65M70 PDFBibTeX XMLCite \textit{D. A. Kopriva}, J. Comput. Phys. 115, No. 1, 184--199 (1994; Zbl 0822.76071) Full Text: DOI
Kopriva, David A. Spectral solution of the viscous blunt-body problem. (English) Zbl 0781.76067 AIAA J. 31, No. 7, 1235-1242 (1993). MSC: 76M25 76K05 65M70 PDFBibTeX XMLCite \textit{D. A. Kopriva}, AIAA J. 31, No. 7, 1235--1242 (1993; Zbl 0781.76067) Full Text: DOI
Kopriva, David A. Spectral solution of inviscid supersonic flows over wedges and axisymmetric cones. (English) Zbl 0753.76135 Comput. Fluids 21, No. 2, 247-266 (1992). MSC: 76M25 76J20 65N35 65M70 PDFBibTeX XMLCite \textit{D. A. Kopriva}, Comput. Fluids 21, No. 2, 247--266 (1992; Zbl 0753.76135) Full Text: DOI
Kopriva, David A. Multidomain spectral solution of the Euler gas-dynamics equations. (English) Zbl 0726.76077 J. Comput. Phys. 96, No. 2, 428-450 (1991). MSC: 76M25 76N15 76H05 76G25 76K05 PDFBibTeX XMLCite \textit{D. A. Kopriva}, J. Comput. Phys. 96, No. 2, 428--450 (1991; Zbl 0726.76077) Full Text: DOI
Kopriva, David A. Computation of hyperbolic equations on complicated domains with patched and overset Chebyshev grids. (English) Zbl 0724.65092 SIAM J. Sci. Stat. Comput. 10, No. 1, 120-132 (1989). MSC: 65M70 65M50 35L45 PDFBibTeX XMLCite \textit{D. A. Kopriva}, SIAM J. Sci. Stat. Comput. 10, No. 1, 120--132 (1989; Zbl 0724.65092) Full Text: DOI
Panchang, V. G.; Kopriva, D. A. Solution of two-dimensional water-wave propagation problems by Chebyshev collocation. (English) Zbl 0692.76005 Math. Comput. Modelling 12, No. 6, 625-640 (1989). MSC: 76B15 35Q30 PDFBibTeX XMLCite \textit{V. G. Panchang} and \textit{D. A. Kopriva}, Math. Comput. Modelling 12, No. 6, 625--640 (1989; Zbl 0692.76005) Full Text: DOI
Kopriva, David A. Domain decomposition with both spectral and finite difference methods for the accurate computation of flows with shocks. (English) Zbl 0678.76059 Appl. Numer. Math. 6, No. 1-2, 141-151 (1989). MSC: 76L05 65N30 76M99 PDFBibTeX XMLCite \textit{D. A. Kopriva}, Appl. Numer. Math. 6, No. 1--2, 141--151 (1989; Zbl 0678.76059) Full Text: DOI
Hussaini, M. Y.; Kopriva, D. A.; Patera, A. T. Spectral collocation methods. (English) Zbl 0671.65093 Appl. Numer. Math. 5, No. 3, 177-208 (1989). Reviewer: G.Hedstrom MSC: 65N35 65-02 35G30 PDFBibTeX XMLCite \textit{M. Y. Hussaini} et al., Appl. Numer. Math. 5, No. 3, 177--208 (1989; Zbl 0671.65093) Full Text: DOI Link
Kopriva, David A. A practical assessment of spectral accuracy for hyperbolic problems with discontinuities. (English) Zbl 0666.65080 J. Sci. Comput. 2, No. 3, 249-262 (1987). MSC: 65N35 35L50 PDFBibTeX XMLCite \textit{D. A. Kopriva}, J. Sci. Comput. 2, No. 3, 249--262 (1987; Zbl 0666.65080) Full Text: DOI
Kopriva, David A. A spectral multidomain method for the solution of hyperbolic systems. (English) Zbl 0601.76087 Appl. Numer. Math. 2, 221-241 (1986). MSC: 76N15 76M99 65N35 PDFBibTeX XMLCite \textit{D. A. Kopriva}, Appl. Numer. Math. 2, 221--241 (1986; Zbl 0601.76087) Full Text: DOI Link
Hussaini, M. Y.; Kopriva, D. A.; Salas, M. D.; Zang, T. A. Spectral methods for the Euler equations: II. Chebyshev methods and shock fitting. (English) Zbl 0587.76125 AIAA J. 23, 234-240 (1985). MSC: 76N15 76M99 76L05 65N35 PDFBibTeX XMLCite \textit{M. Y. Hussaini} et al., AIAA J. 23, 234--240 (1985; Zbl 0587.76125) Full Text: DOI
Hussaini, M. Y.; Kopriva, D. A.; Salas, M. D.; Zang, T. A. Spectral methods for the Euler equations. I. Fourier methods and shock capturing. (English) Zbl 0554.76060 AIAA J. 23, 64-70 (1985). MSC: 76N10 76M99 76L05 85A30 PDFBibTeX XMLCite \textit{M. Y. Hussaini} et al., AIAA J. 23, 64--70 (1985; Zbl 0554.76060) Full Text: DOI