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THE UPWIND OPERATOR SPLITTING finite difference METHOD FOR COMPRESSIBLE TWO-PHASE DISPLACEMENT PROBLEM AND ANALYSIS

Acta Mathematica Scientia 2002年第4期22卷 489-499页

作者：袁益让 Institute of Mathematics Shandong University Jinan 250100 China

For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L 2 norm are derived to determine the error, in the approximate solution.

关键词： two-phase displacement two-dimensional compressibility upwind operator splitting finite difference schemes convergence analysis

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CONVERGENCE RATES FOR difference schemes FOR POLYHEDRAL NONLINEAR PARABOLIC EQUATIONS

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Journal of Computational Mathematics 2010年第4期28卷 474-488页

作者： Adam M.Oberman Department of Mathematics Simon Fraser University

We build finite difference schemes for a class of fully nonlinear parabolic equations. The schemes are polyhedral and grid aligned. While this is a restrictive class of schemes, a wide class of equations are well approximated by equations from this class. For regular （C2,α） solutions of uniformly parabolic equations, we also establish of convergence rate of O（α）. A case study along with supporting numerical results is included.

关键词： Error estimates Convergence rate Viscosity solutions finite difference schemes

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A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrodinger Equations

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Communications in Computational Physics 2008年第9期4卷 729-796页

作者： Xavier Antoine Anton Arnold Christophe Besse Matthias Ehrhardt Achim Schadle Institut Elie Cartan Nancy(IECN) Universite Henri Poincare Nancy 1UMR 7502INRIA CoridaNancy-UniversiteFrance. Institut fur Analysis und Scientific Computing Technische Universitat WienWiedner Hauptstr.81040 WienAustria. Project-Team SIMPAF INRIA Lille Nord Europe Research Centre Laboratoire Paul Painleve U.M.R CNRS 8524 Universite des Sciences et Technologies de LilleFrance. Weierstrass Institute for Applied Analysis and Stochastics Mohrenstr.3910117 BerlinGermany. Zuse-Institut Berlin Takustrasse 714195 BerlinGermany.

In this review article we discuss different techniques to solve numerically the time-dependent Schrodinger equation on unbounded *** present in detail the most recent approaches and describe briefly alternative ideas pointing out the relations between these *** conclude with several numerical examples from different application areas to compare the presented *** mainly focus on the one-dimensional problem but also touch upon the situation in two space dimensions and the cubic nonlinear case.

关键词： Schrodinger equation transparent boundary conditions discrete convolution unbounded domain finite difference schemes finite elements

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A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain

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Communications in Computational Physics 2014年第7期16卷 541-570页

作者： Jan Nordstrom Qaisar Abbas Brittany A.Erickson Hannes Frenander Department of Mathematics Division of Computational MathematicsLinkoping UniversitySE-58183 Link¨opingSweden Department of Information Technology Division of Scientific ComputingUppsala UniversitySE-75105 UppsalaSweden Department of Geological Sciences San Diego State UniversitySan DiegoCA 92182-1020USA Department of Mathematics Division of Computational MathematicsLinkoping UniversitySE-58183 Link¨opingSweden.

A new weak boundary procedure for hyperbolic problems is *** consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that *** new boundary procedure is applied near boundaries in an extended domain where data is *** show how to raise the order of accuracy of the scheme,how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the *** new boundary procedure is cheap,easy to implement and suitable for all numerical methods,not only finite difference methods,that employ weak boundary *** results that corroborate the analysis are presented.

关键词： Summation-by-parts weak boundary conditions penalty technique high-order accuracy finite difference schemes stability steady-state non-reflecting boundary conditions

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