Vassilevski, Yuri; Liogky, Alexey; Salamatova, Victoria How material and geometrical nonlinearity influences diastolic function of an idealized aortic valve. (English) Zbl 1522.74075 Contin. Mech. Thermodyn. 35, No. 4, 1581-1594 (2023). MSC: 74K35 76Z05 PDFBibTeX XMLCite \textit{Y. Vassilevski} et al., Contin. Mech. Thermodyn. 35, No. 4, 1581--1594 (2023; Zbl 1522.74075) Full Text: DOI
Vassilevski, Yu. V.; Terekhov, K. M. Nonlinear finite volume method for the interface advection-compression problem on unstructured adaptive meshes. (English. Russian original) Zbl 1515.76111 Comput. Math. Math. Phys. 62, No. 7, 1041-1058 (2022); translation from Zh. Vychisl. Mat. Mat. Fiz. 62, No. 7, 1067-1084 (2022). MSC: 76M12 76R99 PDFBibTeX XMLCite \textit{Yu. V. Vassilevski} and \textit{K. M. Terekhov}, Comput. Math. Math. Phys. 62, No. 7, 1041--1058 (2022; Zbl 1515.76111); translation from Zh. Vychisl. Mat. Mat. Fiz. 62, No. 7, 1067--1084 (2022) Full Text: DOI
Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V. A finite element scheme for the numerical solution of the Navier-Stokes/Biot coupled problem. (English) Zbl 07543679 Russ. J. Numer. Anal. Math. Model. 37, No. 3, 159-174 (2022). MSC: 65Mxx 76M10 65M12 74F10 76Z05 PDFBibTeX XMLCite \textit{A. Lozovskiy} et al., Russ. J. Numer. Anal. Math. Model. 37, No. 3, 159--174 (2022; Zbl 07543679) Full Text: DOI
Terekhov, Kirill M.; Vassilevski, Yuri V. Finite volume method for coupled subsurface flow problems. II: Poroelasticity. (English) Zbl 07536731 J. Comput. Phys. 462, Article ID 111225, 21 p. (2022). MSC: 65Fxx 65Mxx 65Nxx PDFBibTeX XMLCite \textit{K. M. Terekhov} and \textit{Y. V. Vassilevski}, J. Comput. Phys. 462, Article ID 111225, 21 p. (2022; Zbl 07536731) Full Text: DOI
Vassilevski, Y. V.; Bogdanov, O. N.; Chesnokova, X. V.; Danilov, A. A.; Dobroserdova, T. K.; Dobrovolsky, D. D.; Lozovskiy, A. V. Non-FSI 3D hemodynamic simulations in time-dependent domains. (English) Zbl 1471.92118 Mondaini, Rubem P. (ed.), Trends in biomathematics: chaos and control in epidemics, ecosystems, and cells. Selected works from the 20th BIOMAT consortium lectures, Rio de Janeiro, Brazil, November 1–6, 2020. Cham: Springer. 261-269 (2021). MSC: 92C35 76Z05 PDFBibTeX XMLCite \textit{Y. V. Vassilevski} et al., in: Trends in biomathematics: chaos and control in epidemics, ecosystems, and cells. Selected works from the 20th BIOMAT consortium lectures, Rio de Janeiro, Brazil, November 1--6, 2020. Cham: Springer. 261--269 (2021; Zbl 1471.92118) Full Text: DOI
Nikitin, Kirill; Vassilevski, Yuri; Yanbarisov, Ruslan An implicit scheme for simulation of free surface non-Newtonian fluid flows on dynamically adapted grids. (English) Zbl 1473.65142 Russ. J. Numer. Anal. Math. Model. 36, No. 3, 165-176 (2021). Reviewer: Abdallah Bradji (Annaba) MSC: 65M08 65M06 65M50 76A10 35Q30 35R35 PDFBibTeX XMLCite \textit{K. Nikitin} et al., Russ. J. Numer. Anal. Math. Model. 36, No. 3, 165--176 (2021; Zbl 1473.65142) Full Text: DOI
Simakov, Sergey S.; Timofeev, Alexander E.; Gamilov, Timur M.; Kopylov, Philipp Yu.; Telyshev, Dmitry V.; Vassilevski, Yuri V. Analysis of the impact of left ventricular assist devices on the systemic circulation. (English) Zbl 1458.92047 Russ. J. Numer. Anal. Math. Model. 35, No. 5, 295-314 (2020). MSC: 92C50 92C35 35Q92 PDFBibTeX XMLCite \textit{S. S. Simakov} et al., Russ. J. Numer. Anal. Math. Model. 35, No. 5, 295--314 (2020; Zbl 1458.92047) Full Text: DOI
Salamatova, Victoria Yu.; Liogky, Alexey A.; Karavaikin, Pavel A.; Danilov, Alexander A.; Kopylov, Philipp Y.; Kopytov, German V.; Kosukhin, Oleg N.; Pryamonosov, Roman A.; Shipilov, Anatoly A.; Yurova, Alexandra S.; Vassilevski, Yuri V. Numerical assessment of coaptation for auto-pericardium based aortic valve cusps. (English) Zbl 1431.92013 Russ. J. Numer. Anal. Math. Model. 34, No. 5, 277-287 (2019). MSC: 92C10 74G15 92C50 PDFBibTeX XMLCite \textit{V. Yu. Salamatova} et al., Russ. J. Numer. Anal. Math. Model. 34, No. 5, 277--287 (2019; Zbl 1431.92013) Full Text: DOI
El Khatib, N.; Kafi, O.; Sequeira, A.; Simakov, S.; Vassilevski, Yu.; Volpert, V. Mathematical modelling of atherosclerosis. (English) Zbl 1431.92031 Math. Model. Nat. Phenom. 14, No. 6, Paper No. 603, 25 p. (2019). MSC: 92C32 92C35 35K57 74F10 35Q92 PDFBibTeX XMLCite \textit{N. El Khatib} et al., Math. Model. Nat. Phenom. 14, No. 6, Paper No. 603, 25 p. (2019; Zbl 1431.92031) Full Text: DOI
Konshin, Igor N.; Olshanskii, Maxim A.; Vassilevski, Yuri V. An algebraic solver for the Oseen problem with application to hemodynamics. (English) Zbl 1416.76116 Chetverushkin, B. N. (ed.) et al., Contributions to partial differential equations and applications. Invited papers of the conferences ‘Contributions to partial differential equations’, Université Pierre et Marie Curie, Paris, France, August 31 – September 1, 2015 and ‘Applied and computational mathematics’, University of Houston, Texas, USA, February 26–27, 2016. Cham: Springer. Comput. Methods Appl. Sci. 47, 339-357 (2019). MSC: 76M10 76Z05 65M60 92C35 76D07 PDFBibTeX XMLCite \textit{I. N. Konshin} et al., Comput. Methods Appl. Sci. 47, 339--357 (2019; Zbl 1416.76116) Full Text: DOI
Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V. Analysis and assessment of a monolithic FSI finite element method. (English) Zbl 1411.76068 Comput. Fluids 179, 277-288 (2019). MSC: 76M10 74S05 65M60 74F10 76D05 PDFBibTeX XMLCite \textit{A. Lozovskiy} et al., Comput. Fluids 179, 277--288 (2019; Zbl 1411.76068) Full Text: DOI
Dobroserdova, Tatyana; Liang, Fuyou; Panasenko, Grigory; Vassilevski, Yuri Multiscale models of blood flow in the compliant aortic bifurcation. (English) Zbl 1446.92012 Appl. Math. Lett. 93, 98-104 (2019). MSC: 92-10 76Z05 74F10 92C35 PDFBibTeX XMLCite \textit{T. Dobroserdova} et al., Appl. Math. Lett. 93, 98--104 (2019; Zbl 1446.92012) Full Text: DOI
Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V. A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain. (English) Zbl 1440.76078 Comput. Methods Appl. Mech. Eng. 333, 55-73 (2018). MSC: 76M10 65M60 76D05 PDFBibTeX XMLCite \textit{A. Lozovskiy} et al., Comput. Methods Appl. Mech. Eng. 333, 55--73 (2018; Zbl 1440.76078) Full Text: DOI arXiv
Nikitin, Kirill D.; Terekhov, Kirill M.; Vassilevski, Yuri V. Two methods of surface tension treatment in free surface flow simulations. (English) Zbl 1448.76063 Appl. Math. Lett. 86, 236-242 (2018). MSC: 76D05 76D27 76D45 PDFBibTeX XMLCite \textit{K. D. Nikitin} et al., Appl. Math. Lett. 86, 236--242 (2018; Zbl 1448.76063) Full Text: DOI
Beklemysheva, Katerina A.; Grigoriev, Georgiy K.; Kulberg, Nikolay S.; Petrov, Igor B.; Vasyukov, Aleksey V.; Vassilevski, Yuri V. Numerical simulation of aberrated medical ultrasound signals. (English) Zbl 1405.92132 Russ. J. Numer. Anal. Math. Model. 33, No. 5, 277-288 (2018). MSC: 92C55 65M25 74J20 92-04 PDFBibTeX XMLCite \textit{K. A. Beklemysheva} et al., Russ. J. Numer. Anal. Math. Model. 33, No. 5, 277--288 (2018; Zbl 1405.92132) Full Text: DOI
Salamatova, V. Yu.; Vassilevski, Yu. V.; Wang, L. Finite element models of hyperelastic materials based on a new strain measure. (English. Russian original) Zbl 1460.74083 Differ. Equ. 54, No. 7, 971-978 (2018); translation from Differ. Uravn. 54, No. 7, 988-995 (2018). MSC: 74S05 74B20 PDFBibTeX XMLCite \textit{V. Yu. Salamatova} et al., Differ. Equ. 54, No. 7, 971--978 (2018; Zbl 1460.74083); translation from Differ. Uravn. 54, No. 7, 988--995 (2018) Full Text: DOI
Nikitin, Kirill D.; Olshanskii, Maxim A.; Terekhov, Kirill M.; Vassilevski, Yuri V. A splitting method for free surface flows over partially submerged obstacles. (English) Zbl 1392.65067 Russ. J. Numer. Anal. Math. Model. 33, No. 2, 95-110 (2018). MSC: 65F10 65N22 65F50 PDFBibTeX XMLCite \textit{K. D. Nikitin} et al., Russ. J. Numer. Anal. Math. Model. 33, No. 2, 95--110 (2018; Zbl 1392.65067) Full Text: DOI
Chernyshenko, Alexey Y.; Olshanskii, Maxim A.; Vassilevski, Yuri V. A hybrid finite volume – finite element method for bulk-surface coupled problems. (English) Zbl 1375.76098 J. Comput. Phys. 352, 516-533 (2018). MSC: 76M12 76M10 76S05 65M08 65M06 PDFBibTeX XMLCite \textit{A. Y. Chernyshenko} et al., J. Comput. Phys. 352, 516--533 (2018; Zbl 1375.76098) Full Text: DOI arXiv
Grigoriev, Fedor Vladimirovich; Kapyrin, Ivan Viktorovich; Vassilevskiĭ, Yuriĭ Viktorovich Modeling of thermal convection in porous media with volumetric heat source using the GeRa code. (Russian. English summary) Zbl 1437.65165 Chebyshevskiĭ Sb. 18, No. 3(63), 235-254 (2017). MSC: 65N08 65M06 76S05 80A19 86A05 35B40 35Q86 PDFBibTeX XMLCite \textit{F. V. Grigoriev} et al., Chebyshevskiĭ Sb. 18, No. 3(63), 235--254 (2017; Zbl 1437.65165) Full Text: DOI MNR Link
Kramarenko, Vasiliy; Nikitin, Kirill; Vassilevski, Yuri A finite volume scheme with improved well modeling in subsurface flow simulation. (English) Zbl 1396.76059 Comput. Geosci. 21, No. 5-6, 1023-1033 (2017). MSC: 76M12 65N08 76S05 PDFBibTeX XMLCite \textit{V. Kramarenko} et al., Comput. Geosci. 21, No. 5--6, 1023--1033 (2017; Zbl 1396.76059) Full Text: DOI
Nikitin, Kirill D.; Olshanskii, Maxim A.; Terekhov, Kirill M.; Vassilevski, Yuri V.; Yanbarisov, Ruslan M. An adaptive numerical method for free surface flows passing rigidly mounted obstacles. (English) Zbl 1410.76255 Comput. Fluids 148, 56-68 (2017). MSC: 76M12 65M08 74F10 76D05 PDFBibTeX XMLCite \textit{K. D. Nikitin} et al., Comput. Fluids 148, 56--68 (2017; Zbl 1410.76255) Full Text: DOI arXiv
Vassilevski, Yuri V.; Beklemysheva, Katerina A.; Grigoriev, Georgiy K.; Kulberg, Nikolay S.; Petrov, Igor B.; Vasyukov, Aleksey V. Numerical modelling of medical ultrasound: phantom-based verification. (English) Zbl 1379.92028 Russ. J. Numer. Anal. Math. Model. 32, No. 5, 339-346 (2017). MSC: 92C55 65M25 PDFBibTeX XMLCite \textit{Y. V. Vassilevski} et al., Russ. J. Numer. Anal. Math. Model. 32, No. 5, 339--346 (2017; Zbl 1379.92028) Full Text: DOI
Chernyshenko, Alexey; Olshahskii, Maxim; Vassilevski, Yuri A hybrid finite volume – finite element method for modeling flows in fractured media. (English) Zbl 1365.76110 Cancès, Clément (ed.) et al., Finite volumes for complex applications VIII – hyperbolic, elliptic and parabolic problems. FVCA 8, Lille, France, June 12–16, 2017. Cham: Springer (ISBN 978-3-319-57393-9/hbk; 978-3-319-57394-6/ebook; 978-3-319-58818-6/set). Springer Proceedings in Mathematics & Statistics 200, 527-535 (2017). MSC: 76M10 76M12 76S05 65M60 65N08 PDFBibTeX XMLCite \textit{A. Chernyshenko} et al., Springer Proc. Math. Stat. 200, 527--535 (2017; Zbl 1365.76110) Full Text: DOI
Kramarenko, Vasiliy; Nikitin, Kirill; Vassilevski, Yuri A nonlinear correction FV scheme for near-well regions. (English) Zbl 1365.76160 Cancès, Clément (ed.) et al., Finite volumes for complex applications VIII – hyperbolic, elliptic and parabolic problems. FVCA 8, Lille, France, June 12–16, 2017. Cham: Springer (ISBN 978-3-319-57393-9/hbk; 978-3-319-57394-6/ebook; 978-3-319-58818-6/set). Springer Proceedings in Mathematics & Statistics 200, 507-516 (2017). MSC: 76M12 35Q35 65M08 65N08 PDFBibTeX XMLCite \textit{V. Kramarenko} et al., Springer Proc. Math. Stat. 200, 507--516 (2017; Zbl 1365.76160) Full Text: DOI
Bessonov, N.; Sequeira, A.; Simakov, S.; Vassilevskii, Yu.; Volpert, V. Methods of blood flow modelling. (English) Zbl 1384.92024 Math. Model. Nat. Phenom. 11, No. 1, 1-25 (2016); erratum ibid. 11, 1, 91 (2016). MSC: 92C35 76M12 76Z05 PDFBibTeX XMLCite \textit{N. Bessonov} et al., Math. Model. Nat. Phenom. 11, No. 1, 1--25 (2016; Zbl 1384.92024) Full Text: DOI
Nikitin, K.; Novikov, K.; Vassilevski, Yuri Nonlinear finite volume method with discrete maximum principle for the two-phase flow model. (English) Zbl 1388.76184 Lobachevskii J. Math. 37, No. 5, 570-581 (2016). MSC: 76M12 65N08 35B50 35Q35 76S05 PDFBibTeX XMLCite \textit{K. Nikitin} et al., Lobachevskii J. Math. 37, No. 5, 570--581 (2016; Zbl 1388.76184) Full Text: DOI
Vassilevski, Yuri V.; Beklemysheva, Katerina A.; Grigoriev, Georgiy K.; Kazakov, Alexander O.; Kulberg, Nikolay S.; Petrov, Igor B.; Salamatova, Victoria Yu.; Vasyukov, Aleksey V. Transcranial ultrasound of cerebral vessels in silico: proof of concept. (English) Zbl 1349.92090 Russ. J. Numer. Anal. Math. Model. 31, No. 5, 317-328 (2016). MSC: 92C55 PDFBibTeX XMLCite \textit{Y. V. Vassilevski} et al., Russ. J. Numer. Anal. Math. Model. 31, No. 5, 317--328 (2016; Zbl 1349.92090) Full Text: DOI
Lozovskiy, Alexander; Olshanskii, Maxim A.; Salamatova, Victoria; Vassilevski, Yuri V. An unconditionally stable semi-implicit FSI finite element method. (English) Zbl 1423.76256 Comput. Methods Appl. Mech. Eng. 297, 437-454 (2015). MSC: 76M10 65M60 74F10 76D05 76Z05 PDFBibTeX XMLCite \textit{A. Lozovskiy} et al., Comput. Methods Appl. Mech. Eng. 297, 437--454 (2015; Zbl 1423.76256) Full Text: DOI
Vassilevski, Yu. V.; Salamatova, V. Yu.; Simakov, S. S. On the elasticity of blood vessels in one-dimensional problems of hemodynamics. (English. Russian original) Zbl 1446.92026 Comput. Math. Math. Phys. 55, No. 9, 1567-1578 (2015); translation from Zh. Vychisl. Mat. Mat. Fiz. 55, No. 9, 1599-1610 (2015). MSC: 92-10 92C35 76Z05 PDFBibTeX XMLCite \textit{Yu. V. Vassilevski} et al., Comput. Math. Math. Phys. 55, No. 9, 1567--1578 (2015; Zbl 1446.92026); translation from Zh. Vychisl. Mat. Mat. Fiz. 55, No. 9, 1599--1610 (2015) Full Text: DOI
Konshin, Igor N.; Olshanskii, Maxim A.; Vassilevski, Yuri V. ILU preconditioners for nonsymmetric saddle-point matrices with application to the incompressible Navier-Stokes equations. (English) Zbl 1326.76061 SIAM J. Sci. Comput. 37, No. 5, A2171-A2197 (2015). MSC: 76M10 65F08 65F10 65N22 65F50 76Z05 76D05 PDFBibTeX XMLCite \textit{I. N. Konshin} et al., SIAM J. Sci. Comput. 37, No. 5, A2171--A2197 (2015; Zbl 1326.76061) Full Text: DOI
Danilov, Alexander; Nikitin, Kirill; Olshanskii, Maxim; Terekhov, Kirill; Vassilevski, Yuri A unified approach for computing tsunami, waves, floods, and landslides. (English) Zbl 1320.86002 Abdulle, Assyr (ed.) et al., Numerical mathematics and advanced applications – ENUMATH 2013. Proceedings of ENUMATH 2013, the 10th European conference on numerical mathematics and advanced applications, Lausanne, Switzerland, August 26–30, 2013. Cham: Springer (ISBN 978-3-319-10704-2/hbk; 978-3-319-10705-9/ebook). Lecture Notes in Computational Science and Engineering 103, 643-650 (2015). MSC: 86A05 76B15 76A05 86-08 PDFBibTeX XMLCite \textit{A. Danilov} et al., Lect. Notes Comput. Sci. Eng. 103, 643--650 (2015; Zbl 1320.86002) Full Text: DOI
Nikitin, Kirill; Terekhov, Kirill; Vassilevski, Yuri A monotone nonlinear finite volume method for diffusion equations and multiphase flows. (English) Zbl 1378.76076 Comput. Geosci. 18, No. 3-4, 311-324 (2014). MSC: 76M20 76T10 65M06 65M50 PDFBibTeX XMLCite \textit{K. Nikitin} et al., Comput. Geosci. 18, No. 3--4, 311--324 (2014; Zbl 1378.76076) Full Text: DOI
Chernyshenko, Alexey; Vassilevski, Yuri A finite volume scheme with the discrete maximum principle for diffusion equations on polyhedral meshes. (English) Zbl 1298.65158 Fuhrmann, Jürgen (ed.) et al., Finite volumes for complex applications VII – methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, Germany, June 15–20, 2014. Vol. I. Cham: Springer (ISBN 978-3-319-05683-8/hbk; 978-3-319-05684-5/ebook; 978-3-319-06402-4/set). Springer Proceedings in Mathematics & Statistics 77, 197-205 (2014). MSC: 65N08 PDFBibTeX XMLCite \textit{A. Chernyshenko} and \textit{Y. Vassilevski}, Springer Proc. Math. Stat. 77, 197--205 (2014; Zbl 1298.65158) Full Text: DOI
Olshanskii, Maxim A.; Terekhov, Kirill M.; Vassilevski, Yuri V. An octree-based solver for the incompressible Navier-Stokes equations with enhanced stability and low dissipation. (English) Zbl 1290.76106 Comput. Fluids 84, 231-246 (2013). MSC: 76M20 76D05 PDFBibTeX XMLCite \textit{M. A. Olshanskii} et al., Comput. Fluids 84, 231--246 (2013; Zbl 1290.76106) Full Text: DOI
Agouzal, Abdellatif; Vassilevski, Yuri V. On the \(L^q\)-saturation property for functions from \(W^{2,p}(\Omega)\). (English) Zbl 1257.46015 Appl. Math. Lett. 25, No. 12, 2123-2127 (2012). MSC: 46E35 41A05 PDFBibTeX XMLCite \textit{A. Agouzal} and \textit{Y. V. Vassilevski}, Appl. Math. Lett. 25, No. 12, 2123--2127 (2012; Zbl 1257.46015) Full Text: DOI
Burdakov, Oleg; Kapyrin, Ivan; Vassilevski, Yuri Monotonicity recovering and accuracy preserving optimization methods for postprocessing finite element solutions. (English) Zbl 1242.65114 J. Comput. Phys. 231, No. 8, 3126-3142 (2012). MSC: 65K05 90C06 90C20 35K20 65M60 PDFBibTeX XMLCite \textit{O. Burdakov} et al., J. Comput. Phys. 231, No. 8, 3126--3142 (2012; Zbl 1242.65114) Full Text: DOI Link
Agouzal, Abdellatif; Lipnikov, Konstantin; Vassilevski, Yuri V. On optimal convergence rate of finite element solutions of boundary value problems on adaptive anisotropic meshes. (English) Zbl 1221.65291 Math. Comput. Simul. 81, No. 10, 1949-1961 (2011). MSC: 65N12 65N15 65N30 65N50 35J25 35Q30 76M10 76D05 76D07 76H05 PDFBibTeX XMLCite \textit{A. Agouzal} et al., Math. Comput. Simul. 81, No. 10, 1949--1961 (2011; Zbl 1221.65291) Full Text: DOI
Tromeur-Dervout, Damien; Vassilevski, Yuri Acceleration of iterative solution of series of systems due to better initial guess. (English) Zbl 1398.65052 Tromeur-Dervout, Damien (ed.) et al., Parallel computational fluid dynamics 2008. Parallel numerical methods, software development and applications. Proceedings of the 20th international conference, Lyon, France, May 19–22, 2008. Berlin: Springer (ISBN 978-3-642-14437-0/hbk; 978-3-642-26515-0/pbk978-3-642-14438-7/ebook). Lecture Notes in Computational Science and Engineering 74, 29-40 (2010). MSC: 65F10 65H10 76M99 76N15 PDFBibTeX XMLCite \textit{D. Tromeur-Dervout} and \textit{Y. Vassilevski}, Lect. Notes Comput. Sci. Eng. 74, 29--40 (2010; Zbl 1398.65052) Full Text: DOI
Agouzal, Abdellatif; Vassilevski, Yuri V. Minimization of gradient errors of piecewise linear interpolation on simplicial meshes. (English) Zbl 1231.65240 Comput. Methods Appl. Mech. Eng. 199, No. 33-36, 2195-2203 (2010). MSC: 65N50 65M50 65D05 PDFBibTeX XMLCite \textit{A. Agouzal} and \textit{Y. V. Vassilevski}, Comput. Methods Appl. Mech. Eng. 199, No. 33--36, 2195--2203 (2010; Zbl 1231.65240) Full Text: DOI
Boursier, Isabelle; Tromeur-Dervout, Damien; Vassilevski, Yuri Parallel solution of mixed finite element/spectral element systems for convection-diffusion equations on non-matching grids. (English) Zbl 1200.65092 Appl. Numer. Math. 60, No. 11, 1131-1147 (2010). MSC: 65N30 PDFBibTeX XMLCite \textit{I. Boursier} et al., Appl. Numer. Math. 60, No. 11, 1131--1147 (2010; Zbl 1200.65092) 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, K.; Svyatskiy, D.; Vassilevski, Y. Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes. (English) Zbl 1158.65083 J. Comput. Phys. 228, No. 3, 703-716 (2009). MSC: 65N30 35J05 65N12 65N50 PDFBibTeX XMLCite \textit{K. Lipnikov} et al., J. Comput. Phys. 228, No. 3, 703--716 (2009; Zbl 1158.65083) Full Text: DOI
Vassilevski, Yu. V.; Dyadechko, V. G.; Lipnikov, K. N. Hessian-based anisotropic mesh adaption in domains with discrete boundaries. (English) Zbl 1080.65115 Russ. J. Numer. Anal. Math. Model. 20, No. 4, 391-402 (2005). Reviewer: Prabhat Kumar Mahanti (Saint John) MSC: 65N50 35J25 65D17 PDFBibTeX XMLCite \textit{Yu. V. Vassilevski} et al., Russ. J. Numer. Anal. Math. Model. 20, No. 4, 391--402 (2005; Zbl 1080.65115) Full Text: DOI
Lipnikov, Konstantin; Vassilevski, Yuri Parallel adaptive solution of 3D boundary value problems by Hessian recovery. (English) Zbl 1025.65057 Comput. Methods Appl. Mech. Eng. 192, No. 11-12, 1495-1513 (2003). MSC: 65N30 65F10 65N50 35J05 65Y05 PDFBibTeX XMLCite \textit{K. Lipnikov} and \textit{Y. Vassilevski}, Comput. Methods Appl. Mech. Eng. 192, No. 11--12, 1495--1513 (2003; Zbl 1025.65057) Full Text: DOI