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 PDFBibTeX XMLCite \textit{K. Lipnikov} et al., J. Comput. Phys. 305, 111--126 (2016; Zbl 1349.65315) Full Text: DOI
Ayuso de Dios, Blanca; Lipnikov, Konstantin; Manzini, Gianmarco The nonconforming virtual element method. (English) Zbl 1343.65140 ESAIM, Math. Model. Numer. Anal. 50, No. 3, 879-904 (2016). Reviewer: Pavol Chocholatý (Bratislava) MSC: 65N30 35J05 65N15 65N06 PDFBibTeX XMLCite \textit{B. Ayuso de Dios} et al., ESAIM, Math. Model. Numer. Anal. 50, No. 3, 879--904 (2016; Zbl 1343.65140) Full Text: DOI arXiv
Lipnikov, K.; Manzini, G. A high-order mimetic method on unstructured polyhedral meshes for the diffusion equation. (English) Zbl 1349.65581 J. Comput. Phys. 272, 360-385 (2014). MSC: 65N08 35J25 PDFBibTeX XMLCite \textit{K. Lipnikov} and \textit{G. Manzini}, J. Comput. Phys. 272, 360--385 (2014; Zbl 1349.65581) Full Text: DOI
Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco; Svyatskiy, Daniil M-adaptation in the mimetic finite difference method. (English) Zbl 1291.65320 Math. Models Methods Appl. Sci. 24, No. 8, 1621-1663 (2014). MSC: 65N06 65N12 65F05 PDFBibTeX XMLCite \textit{V. Gyrya} et al., Math. Models Methods Appl. Sci. 24, No. 8, 1621--1663 (2014; Zbl 1291.65320) Full Text: DOI
Lipnikov, Konstantin; Reynolds, James; Nelson, Eric Mimetic discretization of two-dimensional magnetic diffusion equations. (English) Zbl 1349.78095 J. Comput. Phys. 247, 1-16 (2013). MSC: 78M20 65M06 PDFBibTeX XMLCite \textit{K. Lipnikov} et al., J. Comput. Phys. 247, 1--16 (2013; Zbl 1349.78095) Full Text: DOI
Beirão da Veiga, Lourenço; Lipnikov, Konstantin; Manzini, Gianmarco Arbitrary order nodal mimetic discretizations of elliptic problems on polygonal meshes. (English) Zbl 1246.65201 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, 69-77 (2011). MSC: 65N06 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., Springer Proc. Math. 4, 69--77 (2011; Zbl 1246.65201) Full Text: DOI Link
Beirão da Veiga, L.; Lipnikov, K.; Manzini, G. Arbitrary-order nodal mimetic discretizations of elliptic problems on polygonal meshes. (English) Zbl 1242.65215 SIAM J. Numer. Anal. 49, No. 5, 1737-1760 (2011). Reviewer: Adrian Carabineanu (Bucureşti) MSC: 65N06 65N08 65N12 65N15 65N30 35J05 65N50 PDFBibTeX XMLCite \textit{L. Beirão da Veiga} et al., SIAM J. Numer. Anal. 49, No. 5, 1737--1760 (2011; Zbl 1242.65215) Full Text: DOI Link
Garimella, R. V.; Lipnikov, K. Solution of the diffusion equation in multi-material domains by sub-division of elements along reconstructed interfaces. (English) Zbl 1429.76100 Int. J. Numer. Methods Fluids 65, No. 11-12, 1423-1437 (2011). MSC: 76R50 76T30 65M50 PDFBibTeX XMLCite \textit{R. V. Garimella} and \textit{K. Lipnikov}, Int. J. Numer. Methods Fluids 65, No. 11--12, 1423--1437 (2011; Zbl 1429.76100) Full Text: DOI
Lipnikov, K.; Svyatskiy, D.; Vassilevski, Yu. V. A monotone finite volume method for advection-diffusion equations on unstructured polygonal meshes. (English) Zbl 1192.65140 J. Comput. Phys. 229, No. 11, 4017-4032 (2010). MSC: 65N08 35J25 65N12 65N50 PDFBibTeX XMLCite \textit{K. Lipnikov} et al., J. Comput. Phys. 229, No. 11, 4017--4032 (2010; Zbl 1192.65140) Full Text: DOI
Lipnikov, Konstantin; Shashkov, Mikhail; Svyatskiy, Daniil The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes. (English) Zbl 1120.65332 J. Comput. Phys. 211, No. 2, 473-491 (2006). MSC: 65N06 76M20 65N12 PDFBibTeX XMLCite \textit{K. Lipnikov} et al., J. Comput. Phys. 211, No. 2, 473--491 (2006; Zbl 1120.65332) Full Text: DOI