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Author Index Volume 235 (2011)

2011 Journal of Computational and Applied Mathematics  
Yuan, Nonlinear scheme with high accuracy for nonlinear coupled parabolic-hyperbolic system 3527-3540 Cui, M., High order compact Alternating Direction Implicit method for the generalized sine-Gordon  ...  Chen, A reduced finite volume element formulation and numerical simulations based on POD for parabolic problems 2098-2111 Luxemburg, L.A. and P.R.  ... 
doi:10.1016/s0377-0427(11)00383-9 fatcat:iydszqpkezgivirtbnwhpwere4

The mathematics of finite elements and applications

1989 International Journal of Engineering Science  
For an error estimation, use is made of a new approach which is based on the work of Ainsworth, Wu and the author.  ...  This paper describes theory and methods for developing a posteriori error estimates and an adaptive strategy for hp-finite element approximations of the incompressible Navier-Stokes equations.  ...  We apply these residual-based a posteriori error estimates to two finite volume methods. The first one is the cell vertex finite volume method on structured quadrilateral meshes [1] .  ... 
doi:10.1016/0020-7225(89)90012-8 fatcat:z6hknn325re4tbssbqqzmcketa

Reviews and Descriptions of Tables and Books

1990 Mathematics of Computation  
The book lacks a binding theme and comes across as a potpourri of facts, piled one upon the other. A more modular approach would be highly desirable.  ...  Introductory facts about general curves and surfaces, leading to appropriate representations and data structures for them, and followed by fundamental algorithmic paradigms for manipulating those representations  ...  These volumes are devoted to the solution of systems of equations that arise in applying the finite difference method to problems of mathematical physics, mainly to boundary value problems for second-order  ... 
doi:10.1090/s0025-5718-90-99785-6 fatcat:54iiokhdvzgrtmsscxo3o3gmcq

Numerical Stabilization of the Melt Front for Laser Beam Cutting [chapter]

Torsten Adolph, Willi Schönauer, Markus Niessen, Wolfgang Schulz
2010 Numerical Mathematics and Advanced Applications 2009  
The model is based on Navier-Stokes equations for viscous incompressible flow and convection-diffusion equation describing pollution transport.  ...  The solution is obtained by means of Finite Element Method (FEM).  ...  High-order finite volume methods for nonconservative hyperbolic systems In recent years, there have been increasing interest in the development of high-order numerical methods for nonlinear hyperbolic  ... 
doi:10.1007/978-3-642-11795-4_6 fatcat:nx4nvuxaxfbcdjknopny53ck5e

Development and validation of a SUPG finite element scheme for the compressible Navier–Stokes equations using a modified inviscid flux discretization

Benjamin S. Kirk, Graham F. Carey
2008 International Journal for Numerical Methods in Fluids  
Validation of the finite element formulation via comparisons to experimental data for high-Mach number perfect gas laminar flows is presented, with a specific focus on comparisons to experimentally measured  ...  The spatial discretization, including a modified approach for interpolating the inviscid flux terms in the SUPG finite element formulation, and the 2 nd -order accurate time discretization are presented  ...  For this class of flows the Navier-Stokes equations form a mixed parabolic-hyperbolic set of partial differential equations.  ... 
doi:10.1002/fld.1635 fatcat:ffkopzvbobhbpiby5c5wvrhpqe

Meshless techniques for anisotropic diffusion

Annamaria Mazzia, Giorgio Pini, Flavio Sartoretto
2014 Applied Mathematics and Computation  
The latter would allow better use of parallel computers, since time-stepping is essentially a serial process. Moreover, it would be good for the methods to be of high order accuracy.  ...  A good numerical method would be locally mass conservative, produce no or minimal over/under-shoots, produce minimal numerical diffusion, and require no CFL time-step limit for stability.  ...  We show how to solve the equations using a global implicit approach in an efficient way, and we present the derived computational results.  ... 
doi:10.1016/j.amc.2014.03.032 fatcat:c527226gyfgbffnq4p67qxd7wi

Proceedings of the FEniCS Conference 2017

Jack S. Hale
2017 Figshare  
Proceedings of the FEniCS Conference 2017 that took place 12-14 June 2017 at the University of Luxembourg, Luxembourg.You can cite individual articles in the proceedings using the following bibtex as a  ...  of the FEniCS Conference 2017  ...  We argue that the demonstrated efficiency gains of the multi-level method make the approach competitive with alternatives to MC for eigenvalue problems.  ... 
doi:10.6084/m9.figshare.5086369 fatcat:iwajrgqf3nfgzgyloge3f7dz74

Behavior of the Regularized Sampling Inverse Scattering Method at Internal Resonance Frequencies

N. Shelton, K. F. Warnick
2002 Electromagnetic Waves  
The new physical interpretation is based on the multipole expansion of the induced currents at the sampling point. Thus, it is referred to as the multipole-based linear sampling method (MLSM).  ...  NL, as it is presented in [1], has the following advantages over OLS: original nonlinear inverse problem is reduced to a finite sequence of linear ones; resulting linear problem is one-dimensional while  ...  We will use methods based on special solutions and will address two types of them, i.e. the Green's type solutions and the complex geometrical optics type solutions.  ... 
doi:10.2528/pier02092502 fatcat:d2xx2q47qngnzewhh6lgs66iru

Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics

José María Martí, Ewald Müller
2015 Living Reviews in Computational Astrophysics  
Special emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods.  ...  An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and magnetohydrodynamics (RMHD) is presented.  ...  Finite volume and finite difference methods in numerical RHD and RMHD Finite volume methods exploit the integral form of the partial differential conservation equations.  ... 
doi:10.1007/lrca-2015-3 pmid:30652121 pmcid:PMC6319500 fatcat:h4oex6robjbsxkv3ynz2i22kr4

High-order conservative finite difference GLM–MHD schemes for cell-centered MHD

Andrea Mignone, Petros Tzeferacos, Gianluigi Bodo
2010 Journal of Computational Physics  
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions.  ...  The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. (J. Comput.  ...  Extensive numerical testing of the finite difference schemes presented in this paper was made possible by the computational facilities available thanks to the INAF-CINECA agreement.  ... 
doi:10.1016/ fatcat:3noztyhtuzcaradohlkfeb7hqm

Modeling of nonlinear combustion instability in solid propellant rocket motors

Jay N. Levine, Joseph D. Baum
1982 Symposium (International) on Combustion  
The second method, 5 point averaged parabolic interpolation, is the one currently utilized. Carlson, D. J. and Hoglund, P.  ...  A critical investigation of the ability of finite difference integration methods to accurately solve the one-dimensional, nonlinear, two-phase, hyperbolic, equations which govern the propagation of shock  ...  Although not shown herein, good agreement was also obtained between the predicted and measured results for tests 2, 3, 4, 5, and 8.  ... 
doi:10.1016/s0082-0784(82)80252-x fatcat:k7ry4k3iknevng2zefdbhfzntu

ADER-WENO finite volume schemes with space–time adaptive mesh refinement

Michael Dumbser, Olindo Zanotti, Arturo Hidalgo, Dinshaw S. Balsara
2013 Journal of Computational Physics  
We present the first high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions.  ...  The new scheme has been tested over a wide range of examples for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations of compressible gas dynamics and the equations  ...  A.H. thanks Fundación Caja Madrid (Spain) for its financial support by a grant under the programme Becas de movilidad para profesores de las universidades públicas de Madrid.  ... 
doi:10.1016/ fatcat:wtepqkfnvnbfnlynuctzqcggq4

Techniques in Computational Stochastic Dynamic Programming [chapter]

Floyd B. Hanson
1996 Control and Dynamic Systems  
The presentation in this chapter is in the formal manner of classical applied mathematics in order to focus on the methods and their implementation.  ...  Hanson The finite element method has computational and memory advantages. This method requires a smaller number of nodes than the corresponding finite difference method of similar accuracy.  ...  higher order methods on delay differential equations.  ... 
doi:10.1016/s0090-5267(96)80017-x fatcat:7mtk4gtcmfhippn72sjnnox5ke

Nonlinear Tunable Vibrational Response in Hexagonal Boron Nitride [article]

Fadil Iyikanat, Andrea Konečná, F. Javier García de Abajo
2021 arXiv   pre-print
However, the magnitude of nonlinear effects is generally small, thus requiring high optical intensities for their manifestation at the nanoscale.  ...  The strong nonlinear response, low damping, and robustness of hBN polaritons set the stage for the development of applications in light modulation, sensing, and metrology, while triggering the search for  ...  ACKNOWLEDGEMENTS This work has been supported in part by the European Research Council (Advanced Grant 789104-eNANO), the Spanish MINECO (Severo Ochoa CEX2019-000910-S), the Catalan CERCA Program, and  ... 
arXiv:2105.08153v1 fatcat:t3g6ncyiuvg3plbqzwcsetsmpi

An Implicit-Explicit Eulerian Godunov Scheme for Compressible Flow

J.P. Collins, P. Colella, H.M. Glaz
1995 Journal of Computational Physics  
Several numerical results are presented to demonstrate the properties of the method, especially stable numerical shocks at very high CFL numbers and second-order accurate steady states. Cl  ...  The methodology is described for the cases of linear advection, for nonlinear scalar problems, and for gas dynamics.  ...  ACKNOWLEDGMENT The authors thank the referees for their interesting comments and corrections.  ... 
doi:10.1006/jcph.1995.1021 fatcat:m3nhmrv5krhbzgzr4a3ltyvria
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