LEADER 05159nam 2200625Ia 450 001 9910809086803321 005 20240404142826.0 010 $a1-281-95136-6 010 $a9786611951368 010 $a981-279-980-X 035 $a(CKB)1000000000537979 035 $a(EBL)1679510 035 $a(MiAaPQ)EBC1679510 035 $a(WSP)00004781 035 $a(Au-PeEL)EBL1679510 035 $a(CaPaEBR)ebr10255567 035 $a(CaONFJC)MIL195136 035 $a(OCoLC)815754650 035 $a(PPN)164252622 035 $a(EXLCZ)991000000000537979 100 $a20060826d2001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aNumerical methods for viscosity solutions and applications /$feditors, Maurizio Falcone, Charalampos Makridakis 205 $a1st ed. 210 $aSingapore $cWorld Scientific$dc2001 215 $a1 online resource (249 p.) 225 1 $aSeries on advances in mathematics for applied sciences ;$v59 300 $aDescription based upon print version of record. 311 $a981-02-4717-6 320 $aIncludes bibliographical references. 327 $aForeword; CONTENTS; Geometrical Optics and Viscosity Solutions; 1 High frequency waves and WKB method; 2 The Kravtsov-Ludwig method; 3 Multivalued solutions to the eikonal equation and shadow zones; References; Computation of Vorticity Evolution for a Cylindrical Type-II Superconductor Subject to Parallel and Transverse Applied Magnetic Fields; 1 Introduction; 2 The Models; 3 Discretization of the Models; 4 Numerical Computations; References; A Characterization of the Value Function for a Class of Degenerate Control Problems; 1 Introduction; 2 Assumptions and definitions 327 $a3 A characterization of the value function4 Approximation of the value function; References; Some Microstructures in Three Dimensions; 1 Introduction; 2 A three dimensional example; 3 Minimizing sequences; 4 Numerical experiments; References; Convergence of Numerical Schemes for the Approximation of Level Set Solutions to Mean Curvature Flow; 1 Introduction; 2 Background; 3 The Crandall-Lions scheme; 4 Finite element method; References; Optimal Discretization Steps in Semi-Lagrangian Approximation of First-Order PDEs; 1 Introduction; 2 Construction of the schemes and basic convergence theory 327 $a3 Fully discrete second and third order schemes4 Relationship between time and space step; 5 Numerical tests; Conclusions; References; Convergence Past Singularities to the Forced Mean Curvature Flow for a Modified Reaction-Diffusion Approach; 1 Introduction; 2 Approximate Traveling Wave; 3 Viscosity Solutions; 4 Supersolutions; 5 Comparison Lemma; 6 Convergence and interfaces error estimates; References; The Viscosity-Duality Solutions Approach to Geometric Optics for the Helmholtz Equation; 1 Weak solutions to the differential problem; 2 A class of numerical approximations 327 $a3 Numerical results4 Conclusion; References; Adaptive Grid Generation for Evolutive Hamilton-Jacobi-Bellman Equations; 1 Introduction; 2 Discretization in time and space; 3 Error estimation; 4 Implementation details; 5 Numerical examples; References; Solution and Application of Anisotropic Curvature Driven Evolution of Curves (and Surfaces); 1 Introduction; 2 Direct approach using porous-medium like equations; 3 Direct approach by intrinsic heat equations; 4 Solution using level set equation; 5 Phase field approximation of interface motion; References 327 $aAn Adaptive Scheme on Unstructured Grids for the Shape-From-Shading Problem1 Introduction; 2 A fixed grid fully discrete scheme; 3 A local error indicator; 4 The adaptive grid algorithm; 5 Implementation of the algorithm; 6 Numerical experiments; References; On A Posteriori Error Estimation For Constant Obstacle Problems; 1 Introduction; 2 Results and their discussion; 3 Proofs; References 330 $aThe volume contains twelve papers dealing with the approximation of first and second order problems which arise in many fields of application including optimal control, image processing, geometrical optics and front propagation. Some contributions deal with new algorithms and technical issues related to their implementation. Other contributions are more theoretical, dealing with the convergence of approximation schemes. Many test problems have been examined to evaluate the performances of the algorithms. The volume can attract readers involved in the numerical approximation of differential mod 410 0$aSeries on advances in mathematics for applied sciences ;$v59. 606 $aViscosity solutions 606 $aCalculus of variations 615 0$aViscosity solutions. 615 0$aCalculus of variations. 676 $a515 701 $aFalcone$b Maurizio$042497 701 $aMakridakis$b Charalampos$01718496 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910809086803321 996 $aNumerical methods for viscosity solutions and applications$94115508 997 $aUNINA