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A Lagrangian–Eulerian Method on Regular Triangular Grids for Hyperbolic Problems: Error Estimates for the Scalar Case and a Positive Principle for Multidimensional Systems
Strong bounded variation estimates for the multi-dimensional finite volume approximation of scalar conservation laws and application to a tumour growth model
Numerical Approximation of Hyperbolic Systems of Conservation Laws
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On the Conservation Properties in Multiple Scale Coupling and Simulation for Darcy Flow with Hyperbolic-Transport in Complex Flows
Eduardo Abreu, Ciro Díaz, Juan Galvis and John Pérez Multiscale Modeling & Simulation 18(4) 1375 (2020) https://doi.org/10.1137/20M1320250
Error estimate for the upwind scheme for the linear transport equation with boundary data
Error estimate for the upwind finite volume method for the nonlinear scalar conservation law
Daniel Bouche, Jean-Michel Ghidaglia and Frédéric P. Pascal Journal of Computational and Applied Mathematics 235(18) 5394 (2011) https://doi.org/10.1016/j.cam.2011.05.050
Computational Science and High Performance Computing
D. Kröner Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), Computational Science and High Performance Computing 88 367 (2005) https://doi.org/10.1007/3-540-32376-7_21
Meshfree Methods for Partial Differential Equations
Michael Junk Lecture Notes in Computational Science and Engineering, Meshfree Methods for Partial Differential Equations 26 223 (2003) https://doi.org/10.1007/978-3-642-56103-0_15
Local adaptive methods for convection dominated problems
Robert Klöfkorn, Dietmar Kröner and Mario Ohlberger International Journal for Numerical Methods in Fluids 40(1-2) 79 (2002) https://doi.org/10.1002/fld.268
Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients
Kenneth Hvistendahl Karlsen and Nils Henrik Risebro ESAIM: Mathematical Modelling and Numerical Analysis 35(2) 239 (2001) https://doi.org/10.1051/m2an:2001114
Solution of Equation in ℝn (Part 3), Techniques of Scientific Computing (Part 3)
Robert Eymard, Thierry Gallouët and Raphaèle Herbin Handbook of Numerical Analysis, Solution of Equation in ℝn (Part 3), Techniques of Scientific Computing (Part 3) 7 713 (2000) https://doi.org/10.1016/S1570-8659(00)07005-8
Second-order finite-volume schemes for a non-linear hyperbolic equation: error estimate