Nordbotten, Jan Martin; Keilegavlen, Eirik An introduction to multi-point flux (MPFA) and stress (MPSA) finite volume methods for thermo-poroelasticity. (English) Zbl 1470.74066 Di Pietro, Daniele (ed.) et al., Polyhedral methods in geosciences. Cham: Springer. SEMA SIMAI Springer Ser. 27, 119-158 (2021). MSC: 74S10 76M12 74F05 PDF BibTeX XML Cite \textit{J. M. Nordbotten} and \textit{E. Keilegavlen}, SEMA SIMAI Springer Ser. 27, 119--158 (2021; Zbl 1470.74066) Full Text: DOI arXiv OpenURL
Abushaikha, Ahmad S.; Terekhov, Kirill M. A fully implicit mimetic finite difference scheme for general purpose subsurface reservoir simulation with full tensor permeability. (English) Zbl 1453.76120 J. Comput. Phys. 406, Article ID 109194, 23 p. (2020). MSC: 76M20 76T30 65M06 76S05 PDF BibTeX XML Cite \textit{A. S. Abushaikha} and \textit{K. M. Terekhov}, J. Comput. Phys. 406, Article ID 109194, 23 p. (2020; Zbl 1453.76120) Full Text: DOI OpenURL
Abushaikha, Ahmad S.; Voskov, Denis V.; Tchelepi, Hamdi A. Fully implicit mixed-hybrid finite-element discretization for general purpose subsurface reservoir simulation. (English) Zbl 1378.76042 J. Comput. Phys. 346, 514-538 (2017). MSC: 76M10 76T30 PDF BibTeX XML Cite \textit{A. S. Abushaikha} et al., J. Comput. Phys. 346, 514--538 (2017; Zbl 1378.76042) Full Text: DOI OpenURL
Zhang, Wenjuan; Al Kobaisi, Mohammed A simplified enhanced MPFA formulation for the elliptic equation on general grids. (English) Zbl 1371.65115 Comput. Geosci. 21, No. 4, 621-643 (2017). MSC: 65N08 35J25 65N55 PDF BibTeX XML Cite \textit{W. Zhang} and \textit{M. Al Kobaisi}, Comput. Geosci. 21, No. 4, 621--643 (2017; Zbl 1371.65115) Full Text: DOI OpenURL
Nordbotten, Jan Martin Stable cell-centered finite volume discretization for Biot equations. (English) Zbl 1382.76187 SIAM J. Numer. Anal. 54, No. 2, 942-968 (2016). MSC: 76M12 65N08 65N12 76S05 PDF BibTeX XML Cite \textit{J. M. Nordbotten}, SIAM J. Numer. Anal. 54, No. 2, 942--968 (2016; Zbl 1382.76187) Full Text: DOI arXiv OpenURL
Negara, Ardiansyah; Salama, Amgad; Sun, Shuyu Multiphase flow simulation with gravity effect in anisotropic porous media using multipoint flux approximation. (English) Zbl 1390.76601 Comput. Fluids 114, 66-74 (2015). MSC: 76M20 76S05 76Txx PDF BibTeX XML Cite \textit{A. Negara} et al., Comput. Fluids 114, 66--74 (2015; Zbl 1390.76601) Full Text: DOI Link OpenURL
Nordbotten, Jan Martin Convergence of a cell-centered finite volume discretization for linear elasticity. (English) Zbl 1330.74171 SIAM J. Numer. Anal. 53, No. 6, 2605-2625 (2015). MSC: 74S10 74B05 65N08 65N12 65N30 PDF BibTeX XML Cite \textit{J. M. Nordbotten}, SIAM J. Numer. Anal. 53, No. 6, 2605--2625 (2015; Zbl 1330.74171) Full Text: DOI arXiv Link OpenURL
Du, ShaoHong; Xie, XiaoPing Convergence of an adaptive mixed finite element method for convection-diffusion-reaction equations. (English) Zbl 1338.65234 Sci. China, Math. 58, No. 6, 1327-1348 (2015). Reviewer: Petr Sváček (Praha) MSC: 65N12 65N30 65N15 65N50 35J25 PDF BibTeX XML Cite \textit{S. Du} and \textit{X. Xie}, Sci. China, Math. 58, No. 6, 1327--1348 (2015; Zbl 1338.65234) Full Text: DOI arXiv OpenURL
Gao, Zhiming; Wu, Jiming A second-order positivity-preserving finite volume scheme for diffusion equations on general meshes. (English) Zbl 1315.65077 SIAM J. Sci. Comput. 37, No. 1, A420-A438 (2015). MSC: 65M08 35K05 65M50 65M12 PDF BibTeX XML Cite \textit{Z. Gao} and \textit{J. Wu}, SIAM J. Sci. Comput. 37, No. 1, A420--A438 (2015; Zbl 1315.65077) Full Text: DOI OpenURL
Alyaev, Sergey; Keilegavlen, Eirik; Nordbotten, Jan Martin Analysis of control volume heterogeneous multiscale methods for single phase flow in porous media. (English) Zbl 1426.76211 Multiscale Model. Simul. 12, No. 1, 335-363 (2014). MSC: 76M10 76S05 PDF BibTeX XML Cite \textit{S. Alyaev} et al., Multiscale Model. Simul. 12, No. 1, 335--363 (2014; Zbl 1426.76211) Full Text: DOI Link OpenURL
Hou, Jiangyong; Sun, Shuyu; Chen, Zhangxin Numerical comparison of robustness of some reduction methods in rough grids. (English) Zbl 1308.76167 Numer. Methods Partial Differ. Equations 30, No. 5, 1484-1506 (2014). MSC: 76M10 76M20 65N30 76S05 PDF BibTeX XML Cite \textit{J. Hou} et al., Numer. Methods Partial Differ. Equations 30, No. 5, 1484--1506 (2014; Zbl 1308.76167) Full Text: DOI OpenURL
Droniou, Jerome Finite volume schemes for diffusion equations: introduction to and review of modern methods. (English) Zbl 1291.65319 Math. Models Methods Appl. Sci. 24, No. 8, 1575-1619 (2014). MSC: 65N06 65N08 65N12 65N15 65N30 PDF BibTeX XML Cite \textit{J. Droniou}, Math. Models Methods Appl. Sci. 24, No. 8, 1575--1619 (2014; Zbl 1291.65319) Full Text: DOI arXiv OpenURL
Du, Shaohong A new residual posteriori error estimates of mixed finite element methods for convection-diffusion-reaction equations. (English) Zbl 1288.65159 Numer. Methods Partial Differ. Equations 30, No. 2, 593-624 (2014). Reviewer: Abdallah Bradji (Annaba) MSC: 65N15 65N30 35J25 PDF BibTeX XML Cite \textit{S. Du}, Numer. Methods Partial Differ. Equations 30, No. 2, 593--624 (2014; Zbl 1288.65159) Full Text: DOI OpenURL
Iliev, Oleg; Printsypar, Galina; Rief, Stefan A two-dimensional model of the pressing section of a paper machine including dynamic capillary effects. (English) Zbl 1359.76194 J. Eng. Math. 83, 81-107 (2013). MSC: 76M12 76T99 76B45 PDF BibTeX XML Cite \textit{O. Iliev} et al., J. Eng. Math. 83, 81--107 (2013; Zbl 1359.76194) Full Text: DOI Link OpenURL
Pal, Mayur; Edwards, Michael G. A family of multi-point flux approximation schemes for general element types in two and three dimensions with convergence performance. (English) Zbl 1253.76125 Int. J. Numer. Methods Fluids 69, No. 11, 1797-1817 (2012). MSC: 76S05 PDF BibTeX XML Cite \textit{M. Pal} and \textit{M. G. Edwards}, Int. J. Numer. Methods Fluids 69, No. 11, 1797--1817 (2012; Zbl 1253.76125) Full Text: DOI OpenURL
Pal, Mayur; Edwards, Michael G. Anisotropy favoring triangulation CVD(MPFA) finite volume approximations. (English) Zbl 1427.76164 Int. J. Numer. Methods Fluids 67, No. 10, 1247-1263 (2011). MSC: 76M12 PDF BibTeX XML Cite \textit{M. Pal} and \textit{M. G. Edwards}, Int. J. Numer. Methods Fluids 67, No. 10, 1247--1263 (2011; Zbl 1427.76164) Full Text: DOI OpenURL
Cao, Yufei; Helmig, Rainer; Wohlmuth, Barbara I. Convergence of the multipoint flux approximation L-method for homogeneous media on uniform grids. (English) Zbl 1428.76112 Numer. Methods Partial Differ. Equations 27, No. 2, 329-350 (2011). MSC: 76M12 76S05 65N12 PDF BibTeX XML Cite \textit{Y. Cao} et al., Numer. Methods Partial Differ. Equations 27, No. 2, 329--350 (2011; Zbl 1428.76112) Full Text: DOI OpenURL
Friis, Helmer A.; Edwards, Michael G. A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids. (English) Zbl 1427.76161 J. Comput. Phys. 230, No. 1, 205-231 (2011). MSC: 76M12 76S05 PDF BibTeX XML Cite \textit{H. A. Friis} and \textit{M. G. Edwards}, J. Comput. Phys. 230, No. 1, 205--231 (2011; Zbl 1427.76161) Full Text: DOI OpenURL
Agélas, Léo; Guichard, Cindy; Masson, Roland Convergence of finite volume MPFA O type schemes for heterogeneous anisotropic diffusion problems on general meshes. (English) Zbl 07536517 Int. J. Finite Vol. 7, No. 2, Article ID hal-00340159, 34 p. (2010). MSC: 65N08 65N12 76M12 76S05 PDF BibTeX XML Cite \textit{L. Agélas} et al., Int. J. Finite Vol. 7, No. 2, Article ID hal-00340159, 34 p. (2010; Zbl 07536517) Full Text: HAL OpenURL
Pal, Mayur; Edwards, Michael G. q-families of CVD(MPFA) schemes on general elements: numerical convergence and the maximum principle. (English) Zbl 1269.76075 Arch. Comput. Methods Eng. 17, No. 2, 137-189 (2010). MSC: 76M12 76S05 76T30 76-02 PDF BibTeX XML Cite \textit{M. Pal} and \textit{M. G. Edwards}, Arch. Comput. Methods Eng. 17, No. 2, 137--189 (2010; Zbl 1269.76075) Full Text: DOI OpenURL
Wu, Jiming; Dai, Zihuan; Gao, Zhiming; Yuan, Guangwei Linearity preserving nine-point schemes for diffusion equation on distorted quadrilateral meshes. (English) Zbl 1187.65119 J. Comput. Phys. 229, No. 9, 3382-3401 (2010). MSC: 65N06 35J25 65N50 PDF BibTeX XML Cite \textit{J. Wu} et al., J. Comput. Phys. 229, No. 9, 3382--3401 (2010; Zbl 1187.65119) Full Text: DOI OpenURL
Fontaine, Vincent; Younes, Anis Computational issues of hybrid and multipoint mixed methods for groundwater flow in anisotropic media. (English) Zbl 1398.76104 Comput. Geosci. 14, No. 1, 171-181 (2010). MSC: 76M10 76S05 PDF BibTeX XML Cite \textit{V. Fontaine} and \textit{A. Younes}, Comput. Geosci. 14, No. 1, 171--181 (2010; Zbl 1398.76104) Full Text: DOI OpenURL
Cao, Yufei; Helmig, Rainer; Wohlmuth, Barbara I. Geometrical interpretation of the multi-point flux approximation L-method. (English) Zbl 1166.76042 Int. J. Numer. Methods Fluids 60, No. 11, 1173-1199 (2009). MSC: 76M25 76T10 76S05 PDF BibTeX XML Cite \textit{Y. Cao} et al., Int. J. Numer. Methods Fluids 60, No. 11, 1173--1199 (2009; Zbl 1166.76042) Full Text: DOI OpenURL
Younes, Anis; Fontaine, Vincent Efficiency of mixed hybrid finite element and multipoint flux approximation methods on quadrangular grids and highly anisotropic media. (English) Zbl 1195.74208 Int. J. Numer. Methods Eng. 76, No. 3, 314-336 (2008). MSC: 74S05 74S30 74F10 74E05 PDF BibTeX XML Cite \textit{A. Younes} and \textit{V. Fontaine}, Int. J. Numer. Methods Eng. 76, No. 3, 314--336 (2008; Zbl 1195.74208) Full Text: DOI OpenURL
Chen, Yuguang; Mallison, Bradley T.; Durlofsky, Louis J. Nonlinear two-point flux approximation for modeling full-tensor effects in subsurface flow simulations. (English) Zbl 1259.76041 Comput. Geosci. 12, No. 3, 317-335 (2008). MSC: 76M25 76S05 PDF BibTeX XML Cite \textit{Y. Chen} et al., Comput. Geosci. 12, No. 3, 317--335 (2008; Zbl 1259.76041) Full Text: DOI OpenURL
Vohralík, Martin Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods. (English) Zbl 1160.65059 Numer. Math. 111, No. 1, 121-158 (2008). Reviewer: Adrian Carabineanu (Bucureşti) MSC: 65N15 65N30 35J25 PDF BibTeX XML Cite \textit{M. Vohralík}, Numer. Math. 111, No. 1, 121--158 (2008; Zbl 1160.65059) Full Text: DOI HAL OpenURL
Younes, Anis; Ackerer, Philippe Solving the advection-dispersion equation with discontinuous Galerkin and multipoint flux approximation methods on unstructured meshes. (English) Zbl 1283.76037 Int. J. Numer. Methods Fluids 58, No. 6, 687-708 (2008). MSC: 76M10 65M60 PDF BibTeX XML Cite \textit{A. Younes} and \textit{P. Ackerer}, Int. J. Numer. Methods Fluids 58, No. 6, 687--708 (2008; Zbl 1283.76037) Full Text: DOI OpenURL
Khattri, Sanjay Kumar Analysing an adaptive finite volume for flow in highly heterogeneous porous medium. (English) Zbl 1161.76037 Int. J. Numer. Methods Heat Fluid Flow 18, No. 2, 237-257 (2008). Reviewer: Titus Petrila (Cluj-Napoca) MSC: 76M12 76S05 PDF BibTeX XML Cite \textit{S. K. Khattri}, Int. J. Numer. Methods Heat Fluid Flow 18, No. 2, 237--257 (2008; Zbl 1161.76037) Full Text: DOI OpenURL
Cueto-Felgueroso, Luis; Colominas, Ignasi High-order finite volume methods and multiresolution reproducing kernels. (English) Zbl 1300.76018 Arch. Comput. Methods Eng. 15, No. 2, 185-228 (2008). MSC: 76M12 76N15 76-02 PDF BibTeX XML Cite \textit{L. Cueto-Felgueroso} and \textit{I. Colominas}, Arch. Comput. Methods Eng. 15, No. 2, 185--228 (2008; Zbl 1300.76018) Full Text: DOI OpenURL
Aavatsmark, I.; Eigestad, G. T.; Mallison, B. T.; Nordbotten, J. M. A compact multipoint flux approximation method with improved robustness. (English) Zbl 1230.65114 Numer. Methods Partial Differ. Equations 24, No. 5, 1329-1360 (2008). MSC: 65N06 35J25 PDF BibTeX XML Cite \textit{I. Aavatsmark} et al., Numer. Methods Partial Differ. Equations 24, No. 5, 1329--1360 (2008; Zbl 1230.65114) Full Text: DOI OpenURL
Edwards, Michael G.; Pal, Mayur Positive-definite \(q\)-families of continuous subcell Darcy-flux CVD(MPFA) finite-volume schemes and the mixed finite element method. (English) Zbl 1236.76035 Int. J. Numer. Methods Fluids 57, No. 4, 355-387 (2008). MSC: 76M12 76M10 76S05 PDF BibTeX XML Cite \textit{M. G. Edwards} and \textit{M. Pal}, Int. J. Numer. Methods Fluids 57, No. 4, 355--387 (2008; Zbl 1236.76035) Full Text: DOI OpenURL
Chen, Qian-Yong; Wan, Jing; Yang, Yahan; Mifflin, Rick T. Enriched multi-point flux approximation for general grids. (English) Zbl 1221.76123 J. Comput. Phys. 227, No. 3, 1701-1721 (2008). MSC: 76M12 76S05 PDF BibTeX XML Cite \textit{Q.-Y. Chen} et al., J. Comput. Phys. 227, No. 3, 1701--1721 (2008; Zbl 1221.76123) Full Text: DOI OpenURL
Aavatsmark, I.; Eigestad, G. T.; Klausen, R. A.; Wheeler, M. F.; Yotov, I. Convergence of a symmetric MPFA method on quadrilateral grids. (English) Zbl 1128.65093 Comput. Geosci. 11, No. 4, 333-345 (2007). MSC: 65N12 35J25 65N30 65N50 PDF BibTeX XML Cite \textit{I. Aavatsmark} et al., Comput. Geosci. 11, No. 4, 333--345 (2007; Zbl 1128.65093) Full Text: DOI Link OpenURL
Nordbotten, J. M.; Aavatsmark, I.; Eigestad, G. T. Monotonicity of control volume methods. (English) Zbl 1215.76090 Numer. Math. 106, No. 2, 255-288 (2007). MSC: 76S05 65N06 65M12 35J25 PDF BibTeX XML Cite \textit{J. M. Nordbotten} et al., Numer. Math. 106, No. 2, 255--288 (2007; Zbl 1215.76090) Full Text: DOI OpenURL
Vohralík, Martin Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes. (English) Zbl 1116.65121 ESAIM, Math. Model. Numer. Anal. 40, No. 2, 367-391 (2006). Reviewer: Dietrich Braess (Bochum) MSC: 65N30 35J25 65M60 35K55 PDF BibTeX XML Cite \textit{M. Vohralík}, ESAIM, Math. Model. Numer. Anal. 40, No. 2, 367--391 (2006; Zbl 1116.65121) Full Text: DOI Numdam EuDML OpenURL
Klausen, Runhild A.; Winther, Ragnar Robust convergence of multi point flux approximation on rough grids. (English) Zbl 1102.76036 Numer. Math. 104, No. 3, 317-337 (2006). MSC: 76M10 76S05 65N12 65N30 PDF BibTeX XML Cite \textit{R. A. Klausen} and \textit{R. Winther}, Numer. Math. 104, No. 3, 317--337 (2006; Zbl 1102.76036) Full Text: DOI Link OpenURL
Pal, Mayur; Edwards, Michael G.; Lamb, Anthony R. Convergence study of a family of flux-continuous, finite volume schemes for the general tensor pressure equation. (English) Zbl 1108.76046 Int. J. Numer. Methods Fluids 51, No. 9-10, 1177 - 1203 (2006). MSC: 76M12 76S05 65N12 PDF BibTeX XML Cite \textit{M. Pal} et al., Int. J. Numer. Methods Fluids 51, No. 9--10, 1177--1203 (2006; Zbl 1108.76046) Full Text: DOI OpenURL
Aavatsmark, I.; Eigestad, G. T. Numerical convergence of the MPFA O-method and U-method for general quadrilateral grids. (English) Zbl 1158.65331 Int. J. Numer. Methods Fluids 51, No. 9-10, 939-961 (2006). MSC: 65M06 35J25 76M25 76S05 PDF BibTeX XML Cite \textit{I. Aavatsmark} and \textit{G. T. Eigestad}, Int. J. Numer. Methods Fluids 51, No. 9--10, 939--961 (2006; Zbl 1158.65331) Full Text: DOI OpenURL
Klausen, R. A.; Russell, T. F. Relationships among some locally conservative discretization methods which handle discontinuous coefficients. (English) Zbl 1124.76030 Comput. Geosci. 8, No. 4, 341-377 (2005). MSC: 76M10 76S05 65N30 65N06 PDF BibTeX XML Cite \textit{R. A. Klausen} and \textit{T. F. Russell}, Comput. Geosci. 8, No. 4, 341--377 (2005; Zbl 1124.76030) Full Text: DOI OpenURL
Nordbotten, Jan Martin; Eigestad, Geir Terje Discretization on quadrilateral grids with improved monotonicity properties. (English) Zbl 1143.76540 J. Comput. Phys. 203, No. 2, 744-760 (2005). MSC: 76M25 PDF BibTeX XML Cite \textit{J. M. Nordbotten} and \textit{G. T. Eigestad}, J. Comput. Phys. 203, No. 2, 744--760 (2005; Zbl 1143.76540) Full Text: DOI OpenURL