Sosa Jones, Giselle; Cappanera, Loïc; Riviere, Beatrice Existence and convergence of a discontinuous Galerkin method for the incompressible three-phase flow problem in porous media. (English) Zbl 07800819 IMA J. Numer. Anal. 43, No. 5, 2714-2747 (2023). MSC: 65L60 65M60 65N30 74F10 PDFBibTeX XMLCite \textit{G. Sosa Jones} et al., IMA J. Numer. Anal. 43, No. 5, 2714--2747 (2023; Zbl 07800819) Full Text: DOI arXiv
Liu, Chen; Masri, Rami; Riviere, Beatrice Convergence of a decoupled splitting scheme for the Cahn-Hilliard-Navier-Stokes system. (English) Zbl 1528.65077 SIAM J. Numer. Anal. 61, No. 6, 2651-2694 (2023). MSC: 65M60 65M06 65N30 65M12 65M15 76T06 76M10 76M20 35Q35 PDFBibTeX XMLCite \textit{C. Liu} et al., SIAM J. Numer. Anal. 61, No. 6, 2651--2694 (2023; Zbl 1528.65077) Full Text: DOI arXiv
Masri, Rami; Shen, Boqian; Riviere, Beatrice Discontinuous Galerkin approximations to elliptic and parabolic problems with a Dirac line source. (English) Zbl 1514.65135 ESAIM, Math. Model. Numer. Anal. 57, No. 2, 585-620 (2023). MSC: 65M60 65M06 65N30 65M12 65M15 35J75 35K10 35R06 PDFBibTeX XMLCite \textit{R. Masri} et al., ESAIM, Math. Model. Numer. Anal. 57, No. 2, 585--620 (2023; Zbl 1514.65135) Full Text: DOI arXiv
Masri, Rami; Kuchta, Miroslav; Riviere, Beatrice Discontinuous Galerkin methods for 3D-1D systems. arXiv:2312.16565 Preprint, arXiv:2312.16565 [math.NA] (2023). MSC: 65N30 65M60 BibTeX Cite \textit{R. Masri} et al., ``Discontinuous Galerkin methods for 3D-1D systems'', Preprint, arXiv:2312.16565 [math.NA] (2023) Full Text: arXiv OA License
Liu, Chen; Riviere, Beatrice; Shen, Jie; Zhang, Xiangxiong A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn-Hilliard-Navier-Stokes system. arXiv:2307.09726 Preprint, arXiv:2307.09726 [math.NA] (2023). MSC: 65K10 65M60 65M12 90C25 BibTeX Cite \textit{C. Liu} et al., ``A simple and efficient convex optimization based bound-preserving high order accurate limiter for Cahn-Hilliard-Navier-Stokes system'', Preprint, arXiv:2307.09726 [math.NA] (2023) Full Text: arXiv OA License
Kirk, Keegan L. A.; Masi, Rami; Riviere, Beatrice Numerical analysis of a hybridized discontinuous Galerkin method for the Cahn-Hilliard problem. arXiv:2302.13896 Preprint, arXiv:2302.13896 [math.NA] (2023). MSC: 65M15 65M60 BibTeX Cite \textit{K. L. A. Kirk} et al., ``Numerical analysis of a hybridized discontinuous Galerkin method for the Cahn-Hilliard problem'', Preprint, arXiv:2302.13896 [math.NA] (2023) Full Text: arXiv OA License
Shen, Boqian; Riviere, Beatrice A sequential discontinuous Galerkin method for two-phase flow in deformable porous media. (English) Zbl 1507.76122 Comput. Methods Appl. Mech. Eng. 399, Article ID 115266, 24 p. (2022). MSC: 76M10 65M60 76S05 76T10 PDFBibTeX XMLCite \textit{B. Shen} and \textit{B. Riviere}, Comput. Methods Appl. Mech. Eng. 399, Article ID 115266, 24 p. (2022; Zbl 1507.76122) Full Text: DOI arXiv
Masri, Rami; Liu, Chen; Riviere, Beatrice A discontinuous Galerkin pressure correction scheme for the incompressible Navier-Stokes equations: stability and convergence. (English) Zbl 1491.65099 Math. Comput. 91, No. 336, 1625-1654 (2022). MSC: 65M60 65M22 65N30 65M12 65M15 76D05 35Q30 PDFBibTeX XMLCite \textit{R. Masri} et al., Math. Comput. 91, No. 336, 1625--1654 (2022; Zbl 1491.65099) Full Text: DOI arXiv
Masri, Rami; Puelz, Charles; Riviere, Beatrice A discontinuous Galerkin method for blood flow and solute transport in one-dimensional vessel networks. (English) Zbl 1499.65511 Commun. Appl. Math. Comput. 4, No. 2, 500-529 (2022). MSC: 65M60 65M12 65M15 65M06 65N15 76U05 76Z05 35Q92 92C35 PDFBibTeX XMLCite \textit{R. Masri} et al., Commun. Appl. Math. Comput. 4, No. 2, 500--529 (2022; Zbl 1499.65511) Full Text: DOI
Liu, Chen; Ray, Deep; Thiele, Christopher; Lin, Lu; Riviere, Beatrice A pressure-correction and bound-preserving discretization of the phase-field method for variable density two-phase flows. (English) Zbl 07524769 J. Comput. Phys. 449, Article ID 110769, 20 p. (2022). MSC: 76Mxx 76Dxx 65Mxx PDFBibTeX XMLCite \textit{C. Liu} et al., J. Comput. Phys. 449, Article ID 110769, 20 p. (2022; Zbl 07524769) Full Text: DOI arXiv
Joshaghani, M. S.; Riviere, B.; Sekachev, M. Maximum-principle-satisfying discontinuous Galerkin methods for incompressible two-phase immiscible flow. (English) Zbl 1507.76110 Comput. Methods Appl. Mech. Eng. 391, Article ID 114550, 31 p. (2022). MSC: 76M10 76S05 76T10 PDFBibTeX XMLCite \textit{M. S. Joshaghani} et al., Comput. Methods Appl. Mech. Eng. 391, Article ID 114550, 31 p. (2022; Zbl 1507.76110) Full Text: DOI arXiv
Thiele, Christopher; Riviere, Beatrice \(p\)-multigrid with partial smoothing: an efficient preconditioner for discontinuous Galerkin discretizations with modal bases. (English) Zbl 1519.65060 J. Comput. Appl. Math. 402, Article ID 113815, 16 p. (2022). Reviewer: Wei Gong (Beijing) MSC: 65N55 65N30 65F08 65Y05 35J05 76S05 74F10 74L10 PDFBibTeX XMLCite \textit{C. Thiele} and \textit{B. Riviere}, J. Comput. Appl. Math. 402, Article ID 113815, 16 p. (2022; Zbl 1519.65060) Full Text: DOI
Girault, Vivette; Riviere, Beatrice; Cappanera, Loic A finite element method for degenerate two-phase flow in porous media. II: Convergence. (English) Zbl 1481.65183 J. Numer. Math. 29, No. 3, 187-219 (2021). MSC: 65M60 65M22 65N30 65M12 65M15 35D30 76S05 76T06 76M10 35Q35 26A33 35R11 PDFBibTeX XMLCite \textit{V. Girault} et al., J. Numer. Math. 29, No. 3, 187--219 (2021; Zbl 1481.65183) Full Text: DOI
Ray, Deep; Liu, Chen; Riviere, Beatrice A discontinuous Galerkin method for a diffuse-interface model of immiscible two-phase flows with soluble surfactant. (English) Zbl 1473.76061 Comput. Geosci. 25, No. 5, 1775-1792 (2021). MSC: 76T06 76M10 76S05 86-08 PDFBibTeX XMLCite \textit{D. Ray} et al., Comput. Geosci. 25, No. 5, 1775--1792 (2021; Zbl 1473.76061) Full Text: DOI arXiv
Girault, Vivette; Riviere, Beatrice; Cappanera, Loic A finite element method for degenerate two-phase flow in porous media. I. Well-posedness. (English) Zbl 1482.65181 J. Numer. Math. 29, No. 2, 81-101 (2021). Reviewer: Kanakadurga Sivakumar (Chennai) MSC: 65M60 65M06 65N30 65M12 76S05 76T06 76T10 PDFBibTeX XMLCite \textit{V. Girault} et al., J. Numer. Math. 29, No. 2, 81--101 (2021; Zbl 1482.65181) Full Text: DOI
Doyle, Bryan; Riviere, Beatrice; Sekachev, Michael A multinumerics scheme for incompressible two-phase flow. (English) Zbl 1506.76110 Comput. Methods Appl. Mech. Eng. 370, Article ID 113213, 20 p. (2020). MSC: 76M12 65M08 65M60 76S05 PDFBibTeX XMLCite \textit{B. Doyle} et al., Comput. Methods Appl. Mech. Eng. 370, Article ID 113213, 20 p. (2020; Zbl 1506.76110) Full Text: DOI
Liu, Chen; Frank, Florian; Thiele, Christopher; Alpak, Faruk O.; Berg, Steffen; Chapman, Walter; Riviere, Beatrice An efficient numerical algorithm for solving viscosity contrast Cahn-Hilliard-Navier-Stokes system in porous media. (English) Zbl 1453.76078 J. Comput. Phys. 400, Article ID 108948, 17 p. (2020). MSC: 76M10 76S05 76T06 76D45 65M60 PDFBibTeX XMLCite \textit{C. Liu} et al., J. Comput. Phys. 400, Article ID 108948, 17 p. (2020; Zbl 1453.76078) Full Text: DOI
Fabien, Maurice S.; Knepley, Matthew G.; Riviere, Beatrice M. Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems. (English) Zbl 1452.65336 J. Numer. Math. 28, No. 3, 161-174 (2020). MSC: 65N30 65N12 65N15 35J15 PDFBibTeX XMLCite \textit{M. S. Fabien} et al., J. Numer. Math. 28, No. 3, 161--174 (2020; Zbl 1452.65336) Full Text: DOI
Fabien, Maurice S.; Knepley, Matthew; Riviere, Beatrice A high order hybridizable discontinuous Galerkin method for incompressible miscible displacement in heterogeneous media. (English) Zbl 1508.65128 Results Appl. Math. 8, Article ID 100089, 14 p. (2020). MSC: 65M60 65N30 65M06 76T06 76S05 86A05 PDFBibTeX XMLCite \textit{M. S. Fabien} et al., Results Appl. Math. 8, Article ID 100089, 14 p. (2020; Zbl 1508.65128) Full Text: DOI arXiv
Thompson, Travis B.; Riviere, Beatrice M.; Knepley, Matthew G. An implicit discontinuous Galerkin method for modeling acute edema and resuscitation in the small intestine. (English) Zbl 1501.92018 Math. Med. Biol. 36, No. 4, 513-548 (2019). MSC: 92C32 92C35 35Q92 65M60 PDFBibTeX XMLCite \textit{T. B. Thompson} et al., Math. Med. Biol. 36, No. 4, 513--548 (2019; Zbl 1501.92018) Full Text: DOI
Liu, Chen; Frank, Florian; Alpak, Faruk O.; Rivière, Béatrice An interior penalty discontinuous Galerkin approach for 3D incompressible Navier-Stokes equation for permeability estimation of porous media. (English) Zbl 1452.76095 J. Comput. Phys. 396, 669-686 (2019). MSC: 76M10 76D05 76S05 65M60 PDFBibTeX XMLCite \textit{C. Liu} et al., J. Comput. Phys. 396, 669--686 (2019; Zbl 1452.76095) Full Text: DOI arXiv
Cappanera, Loïc; Rivière, Béatrice Discontinuous Galerkin method for solving the black-oil problem in porous media. (English) Zbl 1416.76097 Numer. Methods Partial Differ. Equations 35, No. 2, 761-789 (2019). MSC: 76M10 65M60 76S05 76T30 PDFBibTeX XMLCite \textit{L. Cappanera} and \textit{B. Rivière}, Numer. Methods Partial Differ. Equations 35, No. 2, 761--789 (2019; Zbl 1416.76097) Full Text: DOI
Liu, Chen; Frank, Florian; Rivière, Béatrice M. Numerical error analysis for nonsymmetric interior penalty discontinuous Galerkin method of Cahn-Hilliard equation. (English) Zbl 1418.65134 Numer. Methods Partial Differ. Equations 35, No. 4, 1509-1537 (2019). MSC: 65M60 65M06 65M12 65M15 35K41 35K55 35Q35 47H10 PDFBibTeX XMLCite \textit{C. Liu} et al., Numer. Methods Partial Differ. Equations 35, No. 4, 1509--1537 (2019; Zbl 1418.65134) Full Text: DOI
Fabien, Maurice S.; Knepley, Matthew G.; Mills, Richard T.; Rivière, Béatrice M. Manycore parallel computing for a hybridizable discontinuous Galerkin nested multigrid method. (English) Zbl 1412.65129 SIAM J. Sci. Comput. 41, No. 2, C73-C96 (2019). MSC: 65M55 65N30 35J15 65Y05 PDFBibTeX XMLCite \textit{M. S. Fabien} et al., SIAM J. Sci. Comput. 41, No. 2, C73--C96 (2019; Zbl 1412.65129) Full Text: DOI arXiv
Chaabane, Nabil; Rivière, Béatrice A splitting-based finite element method for the Biot poroelasticity system. (English) Zbl 1409.76057 Comput. Math. Appl. 75, No. 7, 2328-2337 (2018). MSC: 76M10 65M60 65M15 76S05 PDFBibTeX XMLCite \textit{N. Chaabane} and \textit{B. Rivière}, Comput. Math. Appl. 75, No. 7, 2328--2337 (2018; Zbl 1409.76057) Full Text: DOI
Frank, Florian; Liu, Chen; Alpak, Faruk O.; Riviere, Beatrice A finite volume/discontinuous Galerkin method for the advective Cahn-Hilliard equation with degenerate mobility on porous domains stemming from micro-CT imaging. (English) Zbl 1405.65104 Comput. Geosci. 22, No. 2, 543-563 (2018). MSC: 65M08 76S05 PDFBibTeX XMLCite \textit{F. Frank} et al., Comput. Geosci. 22, No. 2, 543--563 (2018; Zbl 1405.65104) Full Text: DOI arXiv
Chaabane, N.; Rivière, B.; Sekachev, Mikhail; Calandra, Henri A parallelizable sequential method for the Biot system. (English) Zbl 1407.65181 JNAIAM, J. Numer. Anal. Ind. Appl. Math. 12, No. 3-4, 21-34 (2018). MSC: 65M60 65M06 65M12 65Y05 74F10 76S05 35Q35 PDFBibTeX XMLCite \textit{N. Chaabane} et al., JNAIAM, J. Numer. Anal. Ind. Appl. Math. 12, No. 3--4, 21--34 (2018; Zbl 1407.65181) Full Text: Link
Kanschat, Guido; Riviere, Beatrice A finite element method with strong mass conservation for Biot’s linear consolidation model. (English) Zbl 1407.65192 J. Sci. Comput. 77, No. 3, 1762-1779 (2018). MSC: 65M60 65M12 65M15 35Q74 35Q35 74F10 74S05 PDFBibTeX XMLCite \textit{G. Kanschat} and \textit{B. Riviere}, J. Sci. Comput. 77, No. 3, 1762--1779 (2018; Zbl 1407.65192) Full Text: DOI arXiv
Puelz, Charles; Rivière, Béatrice A priori error estimates of Adams-Bashforth discontinuous Galerkin methods for scalar nonlinear conservation laws. (English) Zbl 1407.65161 J. Numer. Math. 26, No. 3, 151-172 (2018). MSC: 65M12 65M15 65M60 35L65 65L06 35Q92 92C35 PDFBibTeX XMLCite \textit{C. Puelz} and \textit{B. Rivière}, J. Numer. Math. 26, No. 3, 151--172 (2018; Zbl 1407.65161) Full Text: DOI arXiv
Chaabane, Nabil; Girault, Vivette; Riviere, Beatrice; Thompson, Travis A stable enriched Galerkin element for the Stokes problem. (English) Zbl 1395.65072 Appl. Numer. Math. 132, 1-21 (2018). MSC: 65M60 65M15 35Q30 76D05 PDFBibTeX XMLCite \textit{N. Chaabane} et al., Appl. Numer. Math. 132, 1--21 (2018; Zbl 1395.65072) Full Text: DOI
Chaabane, Nabil; Rivière, Béatrice A sequential discontinuous Galerkin method for the coupling of flow and geomechanics. (English) Zbl 1404.65162 J. Sci. Comput. 74, No. 1, 375-395 (2018). MSC: 65M60 65M06 65M12 76S05 74F10 35Q35 35Q74 86A60 PDFBibTeX XMLCite \textit{N. Chaabane} and \textit{B. Rivière}, J. Sci. Comput. 74, No. 1, 375--395 (2018; Zbl 1404.65162) Full Text: DOI
Thiele, Christopher; Araya-Polo, Mauricio; Alpak, Faruk O.; Riviere, Beatrice; Frank, Florian Inexact hierarchical scale separation: a two-scale approach for linear systems from discontinuous Galerkin discretizations. (English) Zbl 1398.65088 Comput. Math. Appl. 74, No. 8, 1769-1778 (2017). MSC: 65F50 65F10 65N30 PDFBibTeX XMLCite \textit{C. Thiele} et al., Comput. Math. Appl. 74, No. 8, 1769--1778 (2017; Zbl 1398.65088) Full Text: DOI
Rivière, Béatrice; Tan, Jun; Thompson, Travis Error analysis of primal discontinuous Galerkin methods for a mixed formulation of the Biot equations. (English) Zbl 1368.65195 Comput. Math. Appl. 73, No. 4, 666-683 (2017). MSC: 65M60 65M15 74L15 92C10 PDFBibTeX XMLCite \textit{B. Rivière} et al., Comput. Math. Appl. 73, No. 4, 666--683 (2017; Zbl 1368.65195) Full Text: DOI
Chaabane, Nabil; Girault, Vivette; Puelz, Charles; Riviere, Beatrice Convergence of IPDG for coupled time-dependent Navier-Stokes and Darcy equations. (English) Zbl 1432.65145 J. Comput. Appl. Math. 324, 25-48 (2017). MSC: 65M60 65M12 76D05 76S05 PDFBibTeX XMLCite \textit{N. Chaabane} et al., J. Comput. Appl. Math. 324, 25--48 (2017; Zbl 1432.65145) Full Text: DOI
Girault, Vivette; Li, Jizhou; Rivière, Beatrice M. Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations. (English) Zbl 1457.76161 Numer. Methods Partial Differ. Equations 33, No. 2, 489-513 (2017). MSC: 76S05 35Q35 65M12 76M10 65M60 PDFBibTeX XMLCite \textit{V. Girault} et al., Numer. Methods Partial Differ. Equations 33, No. 2, 489--513 (2017; Zbl 1457.76161) Full Text: DOI
Puelz, Charles; Čanić, Sunčica; Rivière, Béatrice; Rusin, Craig G. Comparison of reduced models for blood flow using Runge-Kutta discontinuous Galerkin methods. (English) Zbl 1361.92020 Appl. Numer. Math. 115, 114-141 (2017). MSC: 92C35 65N30 PDFBibTeX XMLCite \textit{C. Puelz} et al., Appl. Numer. Math. 115, 114--141 (2017; Zbl 1361.92020) Full Text: DOI arXiv
Dong, Justin; Rivière, Béatrice A semi-implicit method for incompressible three-phase flow in porous media. (English) Zbl 1387.76050 Comput. Geosci. 20, No. 6, 1169-1184 (2016). MSC: 76M10 76S05 76T30 PDFBibTeX XMLCite \textit{J. Dong} and \textit{B. Rivière}, Comput. Geosci. 20, No. 6, 1169--1184 (2016; Zbl 1387.76050) Full Text: DOI
Girault, Vivette; Li, Jizhou; Rivière, Beatrice Strong convergence of discrete DG solutions of the heat equation. (English) Zbl 1352.65290 J. Numer. Math. 24, No. 4, 235-252 (2016). MSC: 65M12 65M60 PDFBibTeX XMLCite \textit{V. Girault} et al., J. Numer. Math. 24, No. 4, 235--252 (2016; Zbl 1352.65290) Full Text: DOI Link
Li, Jizhou; Riviere, Beatrice Numerical solutions of the incompressible miscible displacement equations in heterogeneous media. (English) Zbl 1423.76254 Comput. Methods Appl. Mech. Eng. 292, 107-121 (2015). MSC: 76M10 65M60 74F10 76S05 PDFBibTeX XMLCite \textit{J. Li} and \textit{B. Riviere}, Comput. Methods Appl. Mech. Eng. 292, 107--121 (2015; Zbl 1423.76254) Full Text: DOI
Li, Jizhou; Riviere, Beatrice High order discontinuous Galerkin method for simulating miscible flooding in porous media. (English) Zbl 1391.76732 Comput. Geosci. 19, No. 6, 1251-1268 (2015). MSC: 76S05 76M10 86A05 65N30 PDFBibTeX XMLCite \textit{J. Li} and \textit{B. Riviere}, Comput. Geosci. 19, No. 6, 1251--1268 (2015; Zbl 1391.76732) Full Text: DOI
Li, Jizhou; Riviere, Beatrice; Walkington, Noel Convergence of a high order method in time and space for the miscible displacement equations. (English) Zbl 1327.65176 ESAIM, Math. Model. Numer. Anal. 49, No. 4, 953-976 (2015). MSC: 65M12 65M60 PDFBibTeX XMLCite \textit{J. Li} et al., ESAIM, Math. Model. Numer. Anal. 49, No. 4, 953--976 (2015; Zbl 1327.65176) Full Text: DOI
Riviere, Beatrice; Yang, Xin A domain-based multinumeric method for the steady-state convection-diffusion equation. (English) Zbl 1455.76185 Erhel, Jocelyne (ed.) et al., Domain decomposition methods in science and engineering XXI. Proceedings of the 21st international conference, Inria Rennes Center, France, June 25–29, 2012. Cham: Springer. Lect. Notes Comput. Sci. Eng. 98, 113-125 (2014). MSC: 76S05 65N30 65N08 65N12 PDFBibTeX XMLCite \textit{B. Riviere} and \textit{X. Yang}, Lect. Notes Comput. Sci. Eng. 98, 113--125 (2014; Zbl 1455.76185) Full Text: DOI
Girault, V.; Kanschat, G.; Rivière, B. Error analysis for a monolithic discretization of coupled Darcy and Stokes problems. (English) Zbl 1302.76101 J. Numer. Math. 22, No. 2, 109-142 (2014). MSC: 76M10 65N30 76S05 PDFBibTeX XMLCite \textit{V. Girault} et al., J. Numer. Math. 22, No. 2, 109--142 (2014; Zbl 1302.76101) Full Text: DOI Link
Riviere, Beatrice; Sardar, Shirin Penalty-free discontinuous Galerkin methods for incompressible Navier-Stokes equations. (English) Zbl 1361.76007 Math. Models Methods Appl. Sci. 24, No. 6, 1217-1236 (2014). MSC: 76D05 76M10 65N30 35D30 65N12 PDFBibTeX XMLCite \textit{B. Riviere} and \textit{S. Sardar}, Math. Models Methods Appl. Sci. 24, No. 6, 1217--1236 (2014; Zbl 1361.76007) Full Text: DOI
Riviere, Beatrice Discontinuous finite element methods for coupled surface-subsurface flow and transport problems. (English) Zbl 1426.76300 Feng, Xiaobing (ed.) et al., Recent developments in discontinuous Galerkin finite element methods for partial differential equations. Papers based on the 2012 John H. Barrett memorial lectures, Knoxville, TN, USA, May 9–11, 2012. Cham: Springer. IMA Vol. Math. Appl. 157, 259-279 (2014). MSC: 76M10 76S05 76D05 76D07 65N12 65N15 PDFBibTeX XMLCite \textit{B. Riviere}, IMA Vol. Math. Appl. 157, 259--279 (2014; Zbl 1426.76300) Full Text: DOI
Riviere, Beatrice; Yang, Xin Convergence analysis of a coupled method for time-dependent convection-diffusion equations. (English) Zbl 1283.65085 Numer. Methods Partial Differ. Equations 30, No. 1, 133-157 (2014). Reviewer: H. P. Dikshit (Bhopal) MSC: 65M12 65M08 65M60 65M15 35K20 PDFBibTeX XMLCite \textit{B. Riviere} and \textit{X. Yang}, Numer. Methods Partial Differ. Equations 30, No. 1, 133--157 (2014; Zbl 1283.65085) Full Text: DOI
Liu, Kun; Rivière, Béatrice M. Discontinuous Galerkin methods for elliptic partial differential equations with random coefficients. (English) Zbl 1290.65006 Int. J. Comput. Math. 90, No. 11, 2477-2490 (2013). Reviewer: Gong Guanglu (Beijing) MSC: 65C30 65N30 65N15 65C05 60H15 60H35 35R60 65N12 PDFBibTeX XMLCite \textit{K. Liu} and \textit{B. M. Rivière}, Int. J. Comput. Math. 90, No. 11, 2477--2490 (2013; Zbl 1290.65006) Full Text: DOI Link
Brenner, Susanne C. (ed.); Hoppe, Ronald H. W. (ed.); Rivière, Béatrice (ed.) Theory and applications of discontinuous Galerkin methods. Abstracts from the workshop held February 19–25, 2012. (English) Zbl 1349.00079 Oberwolfach Rep. 9, No. 1, 555-609 (2012). MSC: 00B05 00B25 65-06 65N30 65N55 65K15 65Y10 PDFBibTeX XMLCite \textit{S. C. Brenner} (ed.) et al., Oberwolfach Rep. 9, No. 1, 555--609 (2012; Zbl 1349.00079) Full Text: DOI
Rivière, Beatrice M.; Walkington, Noel J. Convergence of a discontinuous Galerkin method for the miscible displacement equation under low regularity. (English) Zbl 1414.76036 SIAM J. Numer. Anal. 49, No. 3, 1085-1110 (2011). MSC: 76M10 76S05 65M60 35Q35 65M12 PDFBibTeX XMLCite \textit{B. M. Rivière} and \textit{N. J. Walkington}, SIAM J. Numer. Anal. 49, No. 3, 1085--1110 (2011; Zbl 1414.76036) Full Text: DOI
Wihler, Thomas P.; Rivière, Béatrice Discontinuous Galerkin methods for second-order elliptic PDE with low-regularity solutions. (English) Zbl 1228.65227 J. Sci. Comput. 46, No. 2, 151-165 (2011). Reviewer: Gisbert Stoyan (Budapest) MSC: 65N30 35J05 65N12 PDFBibTeX XMLCite \textit{T. P. Wihler} and \textit{B. Rivière}, J. Sci. Comput. 46, No. 2, 151--165 (2011; Zbl 1228.65227) Full Text: DOI Link
Chidyagwai, Prince; Mishev, Ilya; Rivière, Béatrice On the coupling of finite volume and discontinuous Galerkin method for elliptic problems. (English) Zbl 1214.65056 J. Comput. Appl. Math. 235, No. 8, 2193-2204 (2011). Reviewer: Nicolae Pop (Baia Mare) MSC: 65N08 65N30 35J25 65N12 PDFBibTeX XMLCite \textit{P. Chidyagwai} et al., J. Comput. Appl. Math. 235, No. 8, 2193--2204 (2011; Zbl 1214.65056) Full Text: DOI
Kanschat, G.; Rivière, B. A strongly conservative finite element method for the coupling of Stokes and Darcy flow. (English) Zbl 1425.76068 J. Comput. Phys. 229, No. 17, 5933-5943 (2010). MSC: 76D07 76M10 76S05 PDFBibTeX XMLCite \textit{G. Kanschat} and \textit{B. Rivière}, J. Comput. Phys. 229, No. 17, 5933--5943 (2010; Zbl 1425.76068) Full Text: DOI arXiv
Proft, J.; Rivière, B. Discontinuous Galerkin methods for convection-diffusion equations for varying and vanishing diffusivity. (English) Zbl 1482.65186 Int. J. Numer. Anal. Model. 6, No. 4, 533-561 (2009). MSC: 65M60 65M12 PDFBibTeX XMLCite \textit{J. Proft} and \textit{B. Rivière}, Int. J. Numer. Anal. Model. 6, No. 4, 533--561 (2009; Zbl 1482.65186) Full Text: Link
Chidyagwai, Prince; Rivière, Béatrice On the solution of the coupled Navier-Stokes and Darcy equations. (English) Zbl 1230.76023 Comput. Methods Appl. Mech. Eng. 198, No. 47-48, 3806-3820 (2009). MSC: 76M10 76D05 76S05 76M30 PDFBibTeX XMLCite \textit{P. Chidyagwai} and \textit{B. Rivière}, Comput. Methods Appl. Mech. Eng. 198, No. 47--48, 3806--3820 (2009; Zbl 1230.76023) Full Text: DOI
Guzmán, Johnny; Rivière, Béatrice Sub-optimal convergence of non-symmetric discontinuous Galerkin methods for odd polynomial approximations. (English) Zbl 1203.65255 J. Sci. Comput. 40, No. 1-3, 273-280 (2009). MSC: 65N30 PDFBibTeX XMLCite \textit{J. Guzmán} and \textit{B. Rivière}, J. Sci. Comput. 40, No. 1--3, 273--280 (2009; Zbl 1203.65255) Full Text: DOI
Çeşmelioğlu, Ayçıl; Rivière, Béatrice Primal discontinuous Galerkin methods for time-dependent coupled surface and subsurface flow. (English) Zbl 1203.76078 J. Sci. Comput. 40, No. 1-3, 115-140 (2009). MSC: 76M10 76D05 65M60 PDFBibTeX XMLCite \textit{A. Çeşmelioğlu} and \textit{B. Rivière}, J. Sci. Comput. 40, No. 1--3, 115--140 (2009; Zbl 1203.76078) Full Text: DOI
Girault, Vivette; Rivière, Béatrice DG approximation of coupled Navier-Stokes and Darcy equations by Beaver-Joseph-Saffman interface condition. (English) Zbl 1406.76082 SIAM J. Numer. Anal. 47, No. 3, 2052-2089 (2009). MSC: 76S05 65N30 PDFBibTeX XMLCite \textit{V. Girault} and \textit{B. Rivière}, SIAM J. Numer. Anal. 47, No. 3, 2052--2089 (2009; Zbl 1406.76082) Full Text: DOI
Epshteyn, Y.; Khan, T.; Rivière, B. Numerical solution of a one-dimensional inverse problem by the discontinuous Galerkin method. (English) Zbl 1161.65340 Math. Comput. Simul. 79, No. 7, 1989-2000 (2009). MSC: 65L09 34A55 65L60 34A30 PDFBibTeX XMLCite \textit{Y. Epshteyn} et al., Math. Comput. Simul. 79, No. 7, 1989--2000 (2009; Zbl 1161.65340) Full Text: DOI
Epshteyn, Yekaterina; Rivière, Beatrice Analysis of \(hp\) discontinuous Galerkin methods for incompressible two-phase flow. (English) Zbl 1157.76024 J. Comput. Appl. Math. 225, No. 2, 487-509 (2009). MSC: 76M10 76T10 76S05 65M12 65M60 PDFBibTeX XMLCite \textit{Y. Epshteyn} and \textit{B. Rivière}, J. Comput. Appl. Math. 225, No. 2, 487--509 (2009; Zbl 1157.76024) Full Text: DOI
Epshteyn, Yekaterina; Rivière, Beatrice Convergence of high-order methods for miscible displacement. (English) Zbl 1171.76025 Int. J. Numer. Anal. Model. 5, Suppl., 47-63 (2008). MSC: 76M10 76M20 76S05 65M12 65M15 PDFBibTeX XMLCite \textit{Y. Epshteyn} and \textit{B. Rivière}, Int. J. Numer. Anal. Model. 5, 47--63 (2008; Zbl 1171.76025) Full Text: Link
Rivière, Béatrice Discontinuous Galerkin methods for solving elliptic and parabolic equations. Theory and implementation. (English) Zbl 1153.65112 Frontiers in Applied Mathematics 35. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-898716-56-6/pbk; 978-0-89871-744-0/ebook). xxii, 190 p. (2008). Reviewer: Rolf Dieter Grigorieff (Berlin) MSC: 65N30 65-02 65M60 65N40 35Q30 76S05 76M10 74B05 74S05 65M20 65M12 65N12 65M15 65N15 35J25 35K15 76D05 76D07 PDFBibTeX XMLCite \textit{B. Rivière}, Discontinuous Galerkin methods for solving elliptic and parabolic equations. Theory and implementation. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2008; Zbl 1153.65112) Full Text: DOI
Rivière, Béatrice; Shaw, Simon; Whiteman, J. R. Discontinuous Galerkin finite element methods for dynamic linear solid viscoelasticity problems. (English) Zbl 1127.74045 Numer. Methods Partial Differ. Equations 23, No. 5, 1149-1166 (2007). MSC: 74S05 74H15 74D05 65M60 65M15 PDFBibTeX XMLCite \textit{B. Rivière} et al., Numer. Methods Partial Differ. Equations 23, No. 5, 1149--1166 (2007; Zbl 1127.74045) Full Text: DOI
Epshteyn, Yekaterina; Rivière, Béatrice Estimation of penalty parameters for symmetric interior penalty Galerkin methods. (English) Zbl 1141.65078 J. Comput. Appl. Math. 206, No. 2, 843-872 (2007). Reviewer: Petr Sváček (Praha) MSC: 65N30 65N12 35J25 PDFBibTeX XMLCite \textit{Y. Epshteyn} and \textit{B. Rivière}, J. Comput. Appl. Math. 206, No. 2, 843--872 (2007; Zbl 1141.65078) Full Text: DOI
Epshteyn, Y.; Rivière, B. Fully implicit discontinuous finite element methods for two-phase flow. (English) Zbl 1370.76085 Appl. Numer. Math. 57, No. 4, 383-401 (2007). MSC: 76M10 76S05 65M60 76T99 PDFBibTeX XMLCite \textit{Y. Epshteyn} and \textit{B. Rivière}, Appl. Numer. Math. 57, No. 4, 383--401 (2007; Zbl 1370.76085) Full Text: DOI
Rivière, Béatrice; Shaw, Simon Discontinuous Galerkin finite element approximation of nonlinear non-Fickian diffusion in viscoelastic polymers. (English) Zbl 1135.65036 SIAM J. Numer. Anal. 44, No. 6, 2650-2670 (2006). Reviewer: Angela Handlovičová (Bratislava) MSC: 65M60 35K50 35K57 74D10 76A10 76M10 76R50 35A35 PDFBibTeX XMLCite \textit{B. Rivière} and \textit{S. Shaw}, SIAM J. Numer. Anal. 44, No. 6, 2650--2670 (2006; Zbl 1135.65036) Full Text: DOI
Klieber, W.; Rivière, B. Adaptive simulations of two-phase flow by discontinuous Galerkin methods. (English) Zbl 1120.76327 Comput. Methods Appl. Mech. Eng. 196, No. 1-3, 404-419 (2006). MSC: 76M10 76S05 76T30 PDFBibTeX XMLCite \textit{W. Klieber} and \textit{B. Rivière}, Comput. Methods Appl. Mech. Eng. 196, No. 1--3, 404--419 (2006; Zbl 1120.76327) Full Text: DOI
Kaya, Songul; Layton, William; Rivière, Béatrice Subgrid stabilized defect correction methods for the Navier-Stokes equations. (English) Zbl 1124.76029 SIAM J. Numer. Anal. 44, No. 4, 1639-1654 (2006). MSC: 76M10 76D05 65N30 65N15 PDFBibTeX XMLCite \textit{S. Kaya} et al., SIAM J. Numer. Anal. 44, No. 4, 1639--1654 (2006; Zbl 1124.76029) Full Text: DOI
Kaya, Songul; Rivière, Béatrice A two-grid stabilization method for solving the steady-state Navier-Stokes equations. (English) Zbl 1089.76034 Numer. Methods Partial Differ. Equations 22, No. 3, 728-743 (2006). MSC: 76M10 76D05 65N15 65N30 PDFBibTeX XMLCite \textit{S. Kaya} and \textit{B. Rivière}, Numer. Methods Partial Differ. Equations 22, No. 3, 728--743 (2006; Zbl 1089.76034) Full Text: DOI
Kaya, Songul; Rivière, Béatrice A discontinuous subgrid eddy viscosity method for the time-dependent Navier–Stokes equations. (English) Zbl 1096.76026 SIAM J. Numer. Anal. 43, No. 4, 1572-1595 (2005). MSC: 76M10 76D05 65M60 65M15 PDFBibTeX XMLCite \textit{S. Kaya} and \textit{B. Rivière}, SIAM J. Numer. Anal. 43, No. 4, 1572--1595 (2005; Zbl 1096.76026) Full Text: DOI
Girault, Vivette; Rivière, Béatrice; Wheeler, Mary F. A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations. (English) Zbl 1085.76037 ESAIM, Math. Model. Numer. Anal. 39, No. 6, 1115-1147 (2005). MSC: 76M10 76D05 65M15 65M60 PDFBibTeX XMLCite \textit{V. Girault} et al., ESAIM, Math. Model. Numer. Anal. 39, No. 6, 1115--1147 (2005; Zbl 1085.76037) Full Text: DOI Numdam EuDML
Rivière, Béatrice Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problems. (English) Zbl 1065.76143 J. Sci. Comput. 22-23, 479-500 (2005). MSC: 76M10 76D07 76S05 65N15 65N30 PDFBibTeX XMLCite \textit{B. Rivière}, J. Sci. Comput. 22--23, 479--500 (2005; Zbl 1065.76143) Full Text: DOI
Rivière, Béatrice; Yotov, Ivan Locally conservative coupling of Stokes and Darcy flows. (English) Zbl 1084.35063 SIAM J. Numer. Anal. 42, No. 5, 1959-1977 (2005). MSC: 35Q35 65N30 65N15 76D07 76S05 76M10 PDFBibTeX XMLCite \textit{B. Rivière} and \textit{I. Yotov}, SIAM J. Numer. Anal. 42, No. 5, 1959--1977 (2005; Zbl 1084.35063) Full Text: DOI
Rivière, Béatrice Analysis of a multi-numerics/multi-physics problem. (English) Zbl 1216.76033 Feistauer, M. (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2003, the 5th European conference on numerical mathematics and advanced applications, Prague, Czech Republic, August 18–22, 2003. Berlin: Springer (ISBN 3-540-21460-7/hbk). 726-735 (2004). MSC: 76M10 76D07 76S05 65N15 65N30 PDFBibTeX XMLCite \textit{B. Rivière}, in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2003, the 5th European conference on numerical mathematics and advanced applications, Prague, Czech Republic, August 18--22, 2003. Berlin: Springer. 726--735 (2004; Zbl 1216.76033)
Rivière, B.; Wheeler, M. F. A posteriori error estimates for a discontinuous Galerkin method applied to elliptic problems. (English) Zbl 1059.65098 Comput. Math. Appl. 46, No. 1, 141-163 (2003). Reviewer: Fumio Kikuchi (Tokyo) MSC: 65N15 65N30 65N50 35J25 35R05 76M10 76B07 65N12 PDFBibTeX XMLCite \textit{B. Rivière} and \textit{M. F. Wheeler}, Comput. Math. Appl. 46, No. 1, 141--163 (2003; Zbl 1059.65098) Full Text: DOI
Bastian, Peter; Rivière, Béatrice Superconvergence and \(H(div)\) projection for discontinuous Galerkin methods. (English) Zbl 1030.76026 Int. J. Numer. Methods Fluids 42, No. 10, 1043-1057 (2003). MSC: 76M10 76S05 65N12 PDFBibTeX XMLCite \textit{P. Bastian} and \textit{B. Rivière}, Int. J. Numer. Methods Fluids 42, No. 10, 1043--1057 (2003; Zbl 1030.76026) Full Text: DOI
Rivière, Béatrice; Shaw, Simon; Wheeler, Mary F.; Whiteman, John Robert Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity. (English) Zbl 1253.74114 Numer. Math. 95, No. 2, 347-376 (2003). MSC: 74S05 65M60 65R20 74B05 74D05 PDFBibTeX XMLCite \textit{B. Rivière} et al., Numer. Math. 95, No. 2, 347--376 (2003; Zbl 1253.74114) Full Text: DOI
Sun, Shuyu; Rivière, Béatrice; Wheeler, Mary F. A combined mixed finite element and discontinuous Galerkin method for miscible displacement problem in porous media. (English) Zbl 1060.76072 Chan, Tony F. (ed.) et al., Recent progress in computational and applied PDEs. Conference proceedings for the international conference held in Zhangjiajie, China, July 1–7, 2001. New York, NY: Kluwer Academic / Plenum Publishers (ISBN 0-306-47420-4/hbk). 323-351 (2002). MSC: 76M10 76S05 65M60 65M15 PDFBibTeX XMLCite \textit{S. Sun} et al., in: Recent progress in computational and applied PDEs. Conference proceedings for the international conference held in Zhangjiajie, China, July 1--7, 2001. New York, NY: Kluwer Academic / Plenum Publishers. 323--351 (2002; Zbl 1060.76072)
Rivière, Béatrice; Wheeler, Mary Coupling of locally conservative methods for single phase flow. (English) Zbl 1023.76022 Comput. Geosci. 6, No. 3-4, 269-284 (2002). MSC: 76M10 76S05 86A05 PDFBibTeX XMLCite \textit{B. Rivière} and \textit{M. Wheeler}, Comput. Geosci. 6, No. 3--4, 269--284 (2002; Zbl 1023.76022) Full Text: DOI
Rivière, Béatrice; Wheeler, Mary F. Non-conforming methods for transport with nonlinear reaction. (English) Zbl 1068.76053 Chen, Zhangxin (ed.) et al., Fluid flow and transport in porous media: mathematical and numerical treatment. Proceedings of an AMS-IMS-SIAM joint summer research conference, Mount Holyoke College, South Hadley, MA, USA, June 17–21, 2001. Providence, RI: AMS, American Mathematical Society (ISBN 0-8218-2807-X). Contemp. Math. 295, 421-432 (2002). MSC: 76M10 76S05 65M15 65M60 76V05 86A05 PDFBibTeX XMLCite \textit{B. Rivière} and \textit{M. F. Wheeler}, Contemp. Math. 295, 421--432 (2002; Zbl 1068.76053)
Rivière, Béatrice; Wheeler, Mary F. Discontinuous Galerkin methods for flow and transport problems in porous media. (English) Zbl 0996.76056 Commun. Numer. Methods Eng. 18, No. 1, 63-68 (2002). MSC: 76M10 76S05 PDFBibTeX XMLCite \textit{B. Rivière} and \textit{M. F. Wheeler}, Commun. Numer. Methods Eng. 18, No. 1, 63--68 (2002; Zbl 0996.76056) Full Text: DOI
Rivière, Béatrice; Wheeler, Mary F.; Girault, Vivette A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. (English) Zbl 1010.65045 SIAM J. Numer. Anal. 39, No. 3, 902-931 (2001). Reviewer: Ll.G.Chambers (Bangor) MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{B. Rivière} et al., SIAM J. Numer. Anal. 39, No. 3, 902--931 (2001; Zbl 1010.65045) Full Text: DOI
Rivière, Béatrice; Wheeler, Mary F.; Banas, Krzysztof Discontinuous Galerkin method applied to a single phase flow in porous media. II. (English) Zbl 1049.76565 Comput. Geosci. 4, No. 4, 337-349 (2000). MSC: 76M10 65N30 86-08 PDFBibTeX XMLCite \textit{B. Rivière} et al., Comput. Geosci. 4, No. 4, 337--349 (2000; Zbl 1049.76565) Full Text: DOI
Rivière, Béatrice; Wheeler, Mary F. Locally conservative algorithms for flow. (English) Zbl 0990.76045 Whiteman, J. R. (ed.), The mathematics of finite elements and applications X, MAFELAP 1999. Proceedings of the 10th conference, Brunel Univ., Uxbridge, Middlesex, GB, June 22-25, 1999. Amsterdam: Elsevier. 29-46 (2000). MSC: 76M10 76S05 86A05 PDFBibTeX XMLCite \textit{B. Rivière} and \textit{M. F. Wheeler}, in: The mathematics of finite elements and applications X, MAFELAP 1999. Proceedings of the 10th conference, Brunel Univ., Uxbridge, Middlesex, GB, June 22--25, 1999. Amsterdam: Elsevier. 29--46 (2000; Zbl 0990.76045)
Rivière, Béatrice; Wheeler, Mary F. A discontinuous Galerkin method applied to nonlinear parabolic equations. (English) Zbl 0946.65078 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, 231-244 (2000). MSC: 65M60 65M15 35K55 PDFBibTeX XMLCite \textit{B. Rivière} and \textit{M. F. Wheeler}, Lect. Notes Comput. Sci. Eng. 11, 231--244 (2000; Zbl 0946.65078)
Rivière, Béatrice; Wheeler, Mary F.; Girault, Vivette Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I. (English) Zbl 0951.65108 Comput. Geosci. 3, No. 3-4, 337-360 (1999). Reviewer: Ziwen Jiang (Shandong) MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{B. Rivière} et al., Comput. Geosci. 3, No. 3--4, 337--360 (1999; Zbl 0951.65108) Full Text: DOI