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Gander, Martin J.; Halpern, Laurence; Hubert, Florence; Krell, Stella

Optimized Robin transmission conditions for anisotropic diffusion on arbitrary meshes. (English) Zbl 07927647

Dostál, Zdeněk (ed.) et al., Domain decomposition methods in science and engineering XXVII. Selected papers based on the presentations at the 27th international conference on domain decomposition methods, Prague, Czech Republic, July 25–29, 2022. Cham: Springer. Lect. Notes Comput. Sci. Eng. 149, 15-26 (2024).

MSC: 65M55 65N55

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Bonnafont, Thomas; Bessieres, Delphine; Paillol, Jean

A finite volume method to solve the Poisson equation with jump conditions and surface charges: application to electroporation. (English) Zbl 07842850

J. Comput. Phys. 504, Article ID 112862, 22 p. (2024).

MSC: 65Nxx 65Mxx 35Jxx

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Pan, Kejia; Wu, Xiaoxin; Xu, Yufeng

Biquadratic element discrete duality finite volume method for solving elliptic equations on quadrilateral mesh. (English) Zbl 07833843

J. Comput. Phys. 503, Article ID 112857, 16 p. (2024).

MSC: 65Nxx 65Mxx 35Jxx

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Bahari, Mustapha; Quenjel, El-Houssaine; Rhoudaf, Mohamed

Discrete duality finite volume scheme for a generalized Joule heating problem. (English) Zbl 1535.65148

Calcolo 61, No. 1, Paper No. 14, 34 p. (2024).

Reviewer: Abdallah Bradji (Annaba)

MSC: 65M08 65M06 65N08 65N50 65M12 35K65 35K92 80A19 78A55

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Blanc, Xavier; Hoch, Philippe; Lasuen, Clément

Composite finite volume schemes for the diffusion equation on unstructured meshes. (English) Zbl 07801642

Comput. Math. Appl. 156, 207-217 (2024).

MSC: 65-XX 76-XX

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Blanc, Xavier; Hermeline, Francois; Labourasse, Emmanuel; Patela, Julie

Monotonic diamond and DDFV type finite-volume schemes for 2D elliptic problems. (English) Zbl 1519.65047

Commun. Comput. Phys. 34, No. 2, 456-502 (2023).

MSC: 65N08 65N12

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Pan, Kejia; Wu, Xiaoxin; Xu, Yufeng; Yuan, Guangwei

An exact-interface-fitted mesh generator and linearity-preserving finite volume scheme for anisotropic elliptic interface problems. (English) Zbl 07536783

J. Comput. Phys. 463, Article ID 111293, 25 p. (2022).

MSC: 65Nxx 65Mxx 35Jxx

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Gander, Martin J.; Halpern, Laurence; Hubert, Florence; Krell, Stella

Optimized Schwarz methods with general Ventcell transmission conditions for fully anisotropic diffusion with discrete duality finite volume discretizations. (English) Zbl 07836882

Moroccan J. Pure Appl. Anal. 7, No. 2, 182-213 (2021).

MSC: 65N55 65N08 35A35 65F10

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Goudon, Thierry; Krell, Stella; Lissoni, Giulia

Non-overlapping Schwarz algorithms for the incompressible Navier-Stokes equations with DDFV discretizations. (English) Zbl 1491.65081

ESAIM, Math. Model. Numer. Anal. 55, No. 4, 1271-1321 (2021).

Reviewer: Abdallah Bradji (Annaba)

MSC: 65M08 65M06 65N08 65M55 65N50 35Q30 76D05

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Gander, Martin J.; Halpern, Laurence; Hubert, Florence; Krell, Stella

Discrete optimization of Robin transmission conditions for anisotropic diffusion with discrete duality finite volume methods. (English) Zbl 1482.65224

Vietnam J. Math. 49, No. 4, 1349-1378 (2021).

Reviewer: Abdallah Bradji (Annaba)

MSC: 65N55 65N08 65F10 65N12

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El Moutea, Omar; El Amri, Hassan

Combined mixed finite element and nonconforming finite volume methods for flow and transport in porous media. (English) Zbl 1477.65210

Analysis, München 41, No. 3, 123-144 (2021).

MSC: 65N30 76M10 76M12 76S05 76R50

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Ibrahim, Moustafa; Quenjel, El Houssaine; Saad, Mazen

Positive nonlinear DDFV scheme for a degenerate parabolic system describing chemotaxis. (English) Zbl 1524.92021

Comput. Math. Appl. 80, No. 12, 2972-3003 (2020).

MSC: 92C17 65M08 35K65 35K57

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Gander, Martin J.; Halpern, Laurence; Hubert, Florence; Krell, Stella

Optimized overlapping DDFV Schwarz algorithms. (English) Zbl 1454.65180

Klöfkorn, Robert (ed.) et al., Finite volumes for complex applications IX – methods, theoretical aspects, examples. FVCA 9, Bergen, Norway, June 15–19, 2020. In 2 volumes. Volume I and II. Cham: Springer. Springer Proc. Math. Stat. 323, 365-373 (2020).

MSC: 65N55 65N08 65N12 42A38 65Y05

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Chang, Lina; Sheng, Zhiqiang; Yuan, Guangwei

An improvement of the two-point flux approximation scheme on polygonal meshes. (English) Zbl 1452.65305

J. Comput. Phys. 392, 187-204 (2019).

MSC: 65N08 65N50

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Droniou, Jérôme; Eymard, Robert; Prignet, Alain; Talbot, Kyle S.

Unified convergence analysis of numerical schemes for a miscible displacement problem. (English) Zbl 1411.65109

Found. Comput. Math. 19, No. 2, 333-374 (2019).

MSC: 65M06 65M08 65M12 65M60

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Goudon, Thierry; Krell, Stella; Lissoni, Giulia

DDFV method for Navier-Stokes problem with outflow boundary conditions. (English) Zbl 1411.76085

Numer. Math. 142, No. 1, 55-102 (2019).

MSC: 76M12 65M08 35Q30 76D05 65M12

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Su, Shuai; Dong, Qiannan; Wu, Jiming

A decoupled and positivity-preserving discrete duality finite volume scheme for anisotropic diffusion problems on general polygonal meshes. (English) Zbl 1415.65246

J. Comput. Phys. 372, 773-798 (2018).

MSC: 65N08 65N50

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Calgaro, Caterina; Creusé, Emmanuel; Goudon, Thierry; Krell, Stella

Simulations of non homogeneous viscous flows with incompressibility constraints. (English) Zbl 1540.76114

Math. Comput. Simul. 137, 201-225 (2017).

MSC: 76M12 65M08 76D05 76Nxx

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Wu, Jiming

Vertex-centered linearity-preserving schemes for nonlinear parabolic problems on polygonal grids. (English) Zbl 1398.65224

J. Sci. Comput. 71, No. 2, 499-524 (2017).

Reviewer: K. N. Shukla (Gurgaon)

MSC: 65M08

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Gyrya, V.; Lipnikov, K.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor. (English) Zbl 1380.65325

J. Comput. Phys. 348, 549-566 (2017).

MSC: 65N06 76W05 76M20

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Blanc, Xavier; Labourasse, Emmanuel

A positive scheme for diffusion problems on deformed meshes. (English) Zbl 1529.65029

ZAMM, Z. Angew. Math. Mech. 96, No. 6, 660-680 (2016).

MSC: 65M08 35K20 65M12

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Kinfack Jeutsa, A.; Njifenjou, A.; Nganhou, J.

Convergence analysis on unstructured meshes of a DDFV method for flow problems with full Neumann boundary conditions. (English) Zbl 1435.65187

J. Appl. Math. 2016, Article ID 5891064, 22 p. (2016).

MSC: 65N08 65N12

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Camier, Jean-Sylvain; Hermeline, Francois

A monotone nonlinear finite volume method for approximating diffusion operators on general meshes. (English) Zbl 1352.65428

Int. J. Numer. Methods Eng. 107, No. 6, 496-519 (2016).

MSC: 65N08 65N50

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Lipnikov, Konstantin; Manzini, Gianmarco; Moulton, J. David; Shashkov, Mikhail

The mimetic finite difference method for elliptic and parabolic problems with a staggered discretization of diffusion coefficient. (English) Zbl 1349.65315

J. Comput. Phys. 305, 111-126 (2016).

MSC: 65M06 65N06

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Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco

The arbitrary order mixed mimetic finite difference method for the diffusion equation. (English) Zbl 1342.65202

ESAIM, Math. Model. Numer. Anal. 50, No. 3, 851-877 (2016).

Reviewer: Abdallah Bradji (Annaba)

MSC: 65N06 65N12 35J05

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Droniou, Jérome; Eymard, Robert; Herbin, Raphaèle

Gradient schemes: generic tools for the numerical analysis of diffusion equations. (English) Zbl 1346.65042

ESAIM, Math. Model. Numer. Anal. 50, No. 3, 749-781 (2016).

Reviewer: Răzvan Răducanu (Iaşi)

MSC: 65M08 65M12 65M60 35K05

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Droniou, Jérôme; Eymard, Robert

Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations. (English) Zbl 1342.65180

Numer. Math. 132, No. 4, 721-766 (2016).

Reviewer: Pavel Burda (Praha)

MSC: 65M12 35K65 46N40 65M60

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Le, Anh Ha; Omnes, Pascal

An a posteriori error estimation for the discrete duality finite volume discretization of the Stokes equations. (English) Zbl 1321.76046

ESAIM, Math. Model. Numer. Anal. 49, No. 3, 663-693 (2015).

MSC: 76M12 65N08 65N15 76D07

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Chainais-Hillairet, Claire; Krell, Stella; Mouton, Alexandre

Convergence analysis of a DDFV scheme for a system describing miscible fluid flows in porous media. (English) Zbl 1325.76128

Numer. Methods Partial Differ. Equations 31, No. 3, 723-760 (2015).

MSC: 76M12 65N08 76S05

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Delcourte, Sarah; Omnes, Pascal

A discrete duality finite volume discretization of the vorticity-velocity-pressure Stokes problem on almost arbitrary two-dimensional grids. (English) Zbl 1308.76183

Numer. Methods Partial Differ. Equations 31, No. 1, 1-30 (2015).

MSC: 76M12 65N08 65D07 65N15

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Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail

Mimetic finite difference method. (English) Zbl 1352.65420

J. Comput. Phys. 257, Part B, 1163-1227 (2014).

MSC: 65N06 65M06

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Zhang, Zhimin; Zou, Qingsong

A family of finite volume schemes of arbitrary order on rectangular meshes. (English) Zbl 1296.65140

J. Sci. Comput. 58, No. 2, 308-330 (2014).

MSC: 65N08 65N30

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Njifenjou, A.; Donfack, H.; Moukouop-Nguena, I.

Analysis on general meshes of a discrete duality finite volume method for subsurface flow problems. (English) Zbl 1382.76186

Comput. Geosci. 17, No. 2, 391-415 (2013).

MSC: 76M12 76S05 65N08 35Q35

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Sun, Weiwei; Wu, Jiming; Zhang, Xiaoping

A family of linearity-preserving schemes for anisotropic diffusion problems on arbitrary polyhedral grids. (English) Zbl 1286.76138

Comput. Methods Appl. Mech. Eng. 267, 418-433 (2013).

MSC: 76R50 76M12 65N08

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Coudière, Yves; Hubert, Florence; Manzini, Gianmarco

Benchmark 3D: Cevefe-DDFV, a discrete duality scheme with cell/vertex/face+edge unknowns. (English) Zbl 1246.76048

Fořt, Jaroslav (ed.) et al., Finite volumes for complex applications VI: Problems and perspectives. FVCA 6, international symposium, Prague, Czech Republich, June 6–10, 2011. Vol. 1 and 2. Berlin: Springer (ISBN 978-3-642-20670-2/hbk; 978-3-642-20671-9/ebook). Springer Proceedings in Mathematics 4, 977-984 (2011).

MSC: 76M10

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Gao, Zhiming; Wu, Jiming

A linearity-preserving cell-centered scheme for the heterogeneous and anisotropic diffusion equations on general meshes. (English) Zbl 1426.76367

Int. J. Numer. Methods Fluids 67, No. 12, 2157-2183 (2011).

MSC: 76M12 76R50

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Krell, Stella

Stabilized DDFV schemes for Stokes problem with variable viscosity on general 2D meshes. (English) Zbl 1426.76389

Numer. Methods Partial Differ. Equations 27, No. 6, 1666-1706 (2011).

MSC: 76M12 76D07

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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

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Chang, Lina; Yuan, Guangwei

Cell-centered finite volume methods with flexible stencils for diffusion equations on general nonconforming meshes. (English) Zbl 1227.76042

Comput. Methods Appl. Mech. Eng. 198, No. 17-20, 1638-1646 (2009).

MSC: 76M12 76R50

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Eymard, R.; Gallouët, T.; Herbin, R.

Cell centred discretisation of non linear elliptic problems on general multidimensional polyhedral grids. (English) Zbl 1179.65138

J. Numer. Math. 17, No. 3, 173-193 (2009).

Reviewer: Wilhelm Heinrichs (Essen)

MSC: 65N08

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Hermeline, F.

A finite volume method for approximating 3D diffusion operators on general meshes. (English) Zbl 1168.76340

J. Comput. Phys. 228, No. 16, 5763-5786 (2009).

MSC: 76M15 65N30 76A05

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Angot, Philippe; Boyer, Franck; Hubert, Florence

Asymptotic and numerical modelling of flows in fractured porous media. (English) Zbl 1171.76055

ESAIM, Math. Model. Numer. Anal. 43, No. 2, 239-275 (2009).

Reviewer: Ruxandra Stavre (Bucureşti)

MSC: 76S05 76M12 76M45

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Chainais-Hillairet, C.

Discrete duality finite volume schemes for two-dimensional drift-diffusion and energy-transport models. (English) Zbl 1154.82034

Int. J. Numer. Methods Fluids 59, No. 3, 239-257 (2009).

MSC: 82D37 82C70 65M60 65M50 35Q60

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Njifenjou, A.; Kinfack, A. J.

Convergence analysis of an MPFA method for flow problems in anisotropic heterogeneous porous media. (English) Zbl 1490.65244

Int. J. Finite Vol. 5, No. 1, Article ID hal-01120075, 40 p. (2008).

MSC: 65N08 65N12 65N15 76R50

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Hermeline, F.

Approximating second-order vector differential operators on distorted meshes in two space dimensions. (English) Zbl 1195.76264

Int. J. Numer. Methods Eng. 76, No. 7, 1065-1089 (2008).

MSC: 76M12 76D07

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Hermeline, F.; Layouni, S.; Omnes, P.

A finite volume method for the approximation of Maxwell’s equations in two space dimensions on arbitrary meshes. (English) Zbl 1207.78035

J. Comput. Phys. 227, No. 22, 9365-9388 (2008).

MSC: 78M10

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Hermeline, F.

Approximation of 2D and 3D diffusion operators with variable full tensor coefficients on arbitrary meshes. (English) Zbl 1173.76362

Comput. Methods Appl. Mech. Eng. 196, No. 21-24, 2497-2526 (2007).

MSC: 76M12 76R50

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Hermeline, François

A finite volume method for solving Maxwell equations in inhomogeneous media on arbitrary meshes. (English. Abridged French version) Zbl 1070.65074

C. R., Math., Acad. Sci. Paris 339, No. 12, 893-898 (2004).

Reviewer: Vit Dolejsi (Praha)

MSC: 65M06 35Q60 65M50 78A25 78M25

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Found 48 Documents (Results 1–48)

Optimized Robin transmission conditions for anisotropic diffusion on arbitrary meshes. (English) Zbl 07927647

A finite volume method to solve the Poisson equation with jump conditions and surface charges: application to electroporation. (English) Zbl 07842850

Biquadratic element discrete duality finite volume method for solving elliptic equations on quadrilateral mesh. (English) Zbl 07833843

Discrete duality finite volume scheme for a generalized Joule heating problem. (English) Zbl 1535.65148

Composite finite volume schemes for the diffusion equation on unstructured meshes. (English) Zbl 07801642

Monotonic diamond and DDFV type finite-volume schemes for 2D elliptic problems. (English) Zbl 1519.65047

An exact-interface-fitted mesh generator and linearity-preserving finite volume scheme for anisotropic elliptic interface problems. (English) Zbl 07536783

Optimized Schwarz methods with general Ventcell transmission conditions for fully anisotropic diffusion with discrete duality finite volume discretizations. (English) Zbl 07836882

Non-overlapping Schwarz algorithms for the incompressible Navier-Stokes equations with DDFV discretizations. (English) Zbl 1491.65081

Discrete optimization of Robin transmission conditions for anisotropic diffusion with discrete duality finite volume methods. (English) Zbl 1482.65224

Combined mixed finite element and nonconforming finite volume methods for flow and transport in porous media. (English) Zbl 1477.65210

Positive nonlinear DDFV scheme for a degenerate parabolic system describing chemotaxis. (English) Zbl 1524.92021

Optimized overlapping DDFV Schwarz algorithms. (English) Zbl 1454.65180

An improvement of the two-point flux approximation scheme on polygonal meshes. (English) Zbl 1452.65305

Unified convergence analysis of numerical schemes for a miscible displacement problem. (English) Zbl 1411.65109

DDFV method for Navier-Stokes problem with outflow boundary conditions. (English) Zbl 1411.76085

A decoupled and positivity-preserving discrete duality finite volume scheme for anisotropic diffusion problems on general polygonal meshes. (English) Zbl 1415.65246

Simulations of non homogeneous viscous flows with incompressibility constraints. (English) Zbl 1540.76114

Vertex-centered linearity-preserving schemes for nonlinear parabolic problems on polygonal grids. (English) Zbl 1398.65224

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor. (English) Zbl 1380.65325

A positive scheme for diffusion problems on deformed meshes. (English) Zbl 1529.65029

Convergence analysis on unstructured meshes of a DDFV method for flow problems with full Neumann boundary conditions. (English) Zbl 1435.65187

A monotone nonlinear finite volume method for approximating diffusion operators on general meshes. (English) Zbl 1352.65428

The mimetic finite difference method for elliptic and parabolic problems with a staggered discretization of diffusion coefficient. (English) Zbl 1349.65315

The arbitrary order mixed mimetic finite difference method for the diffusion equation. (English) Zbl 1342.65202

Gradient schemes: generic tools for the numerical analysis of diffusion equations. (English) Zbl 1346.65042

Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations. (English) Zbl 1342.65180

An a posteriori error estimation for the discrete duality finite volume discretization of the Stokes equations. (English) Zbl 1321.76046

Convergence analysis of a DDFV scheme for a system describing miscible fluid flows in porous media. (English) Zbl 1325.76128

A discrete duality finite volume discretization of the vorticity-velocity-pressure Stokes problem on almost arbitrary two-dimensional grids. (English) Zbl 1308.76183

Mimetic finite difference method. (English) Zbl 1352.65420

A family of finite volume schemes of arbitrary order on rectangular meshes. (English) Zbl 1296.65140

Analysis on general meshes of a discrete duality finite volume method for subsurface flow problems. (English) Zbl 1382.76186

A family of linearity-preserving schemes for anisotropic diffusion problems on arbitrary polyhedral grids. (English) Zbl 1286.76138

Benchmark 3D: Cevefe-DDFV, a discrete duality scheme with cell/vertex/face+edge unknowns. (English) Zbl 1246.76048

A linearity-preserving cell-centered scheme for the heterogeneous and anisotropic diffusion equations on general meshes. (English) Zbl 1426.76367

Stabilized DDFV schemes for Stokes problem with variable viscosity on general 2D meshes. (English) Zbl 1426.76389

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

Cell-centered finite volume methods with flexible stencils for diffusion equations on general nonconforming meshes. (English) Zbl 1227.76042

Cell centred discretisation of non linear elliptic problems on general multidimensional polyhedral grids. (English) Zbl 1179.65138

A finite volume method for approximating 3D diffusion operators on general meshes. (English) Zbl 1168.76340

Asymptotic and numerical modelling of flows in fractured porous media. (English) Zbl 1171.76055

Discrete duality finite volume schemes for two-dimensional drift-diffusion and energy-transport models. (English) Zbl 1154.82034

Convergence analysis of an MPFA method for flow problems in anisotropic heterogeneous porous media. (English) Zbl 1490.65244

Approximating second-order vector differential operators on distorted meshes in two space dimensions. (English) Zbl 1195.76264

A finite volume method for the approximation of Maxwell’s equations in two space dimensions on arbitrary meshes. (English) Zbl 1207.78035

Approximation of 2D and 3D diffusion operators with variable full tensor coefficients on arbitrary meshes. (English) Zbl 1173.76362

A finite volume method for solving Maxwell equations in inhomogeneous media on arbitrary meshes. (English. Abridged French version) Zbl 1070.65074

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