Partial Differential Equations - Modelling and ... - ResearchGate

More documents

Recommendations

Info

The von Neumann Triple Point Paradox 127 References [BH92] M. Brio and J. K. Hunter. Mach reflection for the two-dimensional Burgers equation. Phys. D, 60:194–207, 1992. [BT49] W. Bleakney and A. H. Taub. Interaction of shock waves. Rev. Modern Physics, 21:584–605, 1949. [CF76] R. Courant and K. O. Friedrichs. Supersonic Flow and Shock Waves. Springer, 1976. [CH90] P. Colella and L. F. Henderson. The von Neumann paradox for the diffraction of weak shock waves. J. Fluid Mech., 213:71–94, 1990. [ČK98] S. Čanić and B. L. Keyfitz. Quasi-one-dimensional Riemann problems and their role in self-similar two-dimensional problems. Arch. Rational Mech. Anal., 144:233–258, 1998. [ČKK01] S. Čanić, B. L. Keyfitz, and E. H. Kim. Mixed hyperbolic-elliptic systems in self-similar flows. Bol. Soc. Bras. Mat., 32:1–23, 2001. [ČKK05] S. Čanić, B. L. Keyfitz, and E. H. Kim. Free boundary problems for nonlinear wave systems: Mach stems for interacting shocks. SIAM J. Math. Anal., 37:1947–1977, 2005. [Gud47] K. G. Guderley. Considerations of the structure of mixed subsonicsupersonic flow patterns. Air Material Command Tech. Report, F-TR-2168-ND, ATI No. 22780, GS-AAF-Wright Field 39, U.S. Wright- Patterson Air Force Base, Dayton, Ohio, October 1947. [Gud62] K. G. Guderley. The Theory of Transonic Flow. Pergamon Press, Oxford, 1962. [HB00] J. K. Hunter and M. Brio. Weak shock reflection. J. Fluid Mech., 410:235–261, 2000. [Hen66] L. F. Henderson. On a class of multi-shock intersections in a perfect gas. Aero. Q., 17:1–20, 1966. [Hen87] L. F. Henderson. Regions and boundaries for diffracting shock wave systems. Z. Angew. Math. Mech., 67:73–86, 1987. [HT04] J. K. Hunter and A. M. Tesdall. Weak shock reflection. In D. Givoli, M. Grote, and G. Papanicolaou, editors, A Celebration of Mathematical Modeling. Kluwer Academic Press, New York, 2004. [KF94] B. L. Keyfitz and M. C. Lopes Filho. A geometric study of shocks in equations that change type. J. Dynam. Differential Equations, 6:351– 393, 1994. [Neu43] J. von Neumann. Oblique reflection of shocks. Explosives Research Report 12, Bureau of Ordinance, 1943. [Neu63] J. von Neumann. CollectedWorks,Vol.6. Pergamon Press, New York, 1963. [Ric81] R. D. Richtmeyer. Principles of Mathematical Physics, Vol. 1. Springer, 1981. [SA05] B. Skews and J. Ashworth. The physical nature of weak shock wave reflection. J. Fluid Mech., 542:105–114, 2005. [Ste59] J. Sternberg. Triple-shock-wave intersections. Phys. Fluids, 2:179–206, 1959. [STS92] A. Sasoh, K. Takayama, and T. Saito. A weak shock wave reflection over wedges. Shock Waves, 2:277–281, 1992. [TH02] A. M. Tesdall and J. K. Hunter. Self-similar solutions for weak shock reflection. SIAM J. Appl. Math., 63:42–61, 2002.
128 R. Sanders and A.M. Tesdall [TR94] E. G. Tabak and R. R. Rosales. Focusing of weak shock waves and the von Neumann paradox of oblique shock reflection. Phys. Fluids, 6:1874–1892, 1994. [TSK06] A. M. Tesdall, R. Sanders, and B. L. Keyfitz. The triple point paradox for the nonlinear wave system. SIAM J. Appl. Math., 67:321–336, 2006. [VK99] E. Vasil’ev and A. Kraiko. Numerical simulation of weak shock diffraction over a wedge under the von Neumann paradox conditions. Comput. Math. Math. Phys., 39:1335–1345, 1999. [ZBHW00] A. Zakharian, M. Brio, J. K. Hunter, and G. Webb. The von Neumann paradox in weak shock reflection. J. Fluid Mech., 422:193–205, 2000.
Page 1 and 2:
Partial Differential Equations
Page 3 and 4:
Partial Differential Equations Mode
Page 5 and 6:
Dedicated to Olivier Pironneau
Page 7 and 8:
VIII Preface computers has been at
Page 9 and 10:
Contents List of Contributors .....
Page 11 and 12:
List of Contributors Yves Achdou UF
Page 13 and 14:
List of Contributors XV Claude Le B
Page 15 and 16:
Discontinuous Galerkin Methods Vive
Page 17 and 18:
Discontinuous Galerkin Methods 5 2
Page 19 and 20:
Discontinuous Galerkin Methods 7 g
Page 21 and 22:
Discontinuous Galerkin Methods 9 (
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Discontinuous Galerkin Methods 15 W
Page 29 and 30:
Let a h and b h denote the bilinear
Page 31 and 32:
Discontinuous Galerkin Methods 19 t
Page 33 and 34:
Discontinuous Galerkin Methods 21 l
Page 35 and 36:
Table 1. Primal DG for transport Di
Page 37 and 38:
Discontinuous Galerkin Methods 25 [
Page 39 and 40:
Mixed Finite Element Methods on Pol
Page 41 and 42:
Mixed FE Methods on Polyhedral Mesh
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
4 Hybridization and Condensation Mi
Page 49 and 50:
Page 51 and 52:
is symmetric and positive definite,
Page 53 and 54:
with some coefficient α ∈ R wher
Page 55 and 56:
44 E.J. Dean and R. Glowinski so fa
Page 57 and 58:
46 E.J. Dean and R. Glowinski 2 A L
Page 59 and 60:
48 E.J. Dean and R. Glowinski S:T=
Page 61 and 62:
50 E.J. Dean and R. Glowinski minim
Page 63 and 64:
52 E.J. Dean and R. Glowinski 6 On
Page 65 and 66:
54 E.J. Dean and R. Glowinski Fig.
Page 67 and 68:
56 E.J. Dean and R. Glowinski and
Page 69 and 70:
58 E.J. Dean and R. Glowinski 7 Num
Page 71 and 72:
60 E.J. Dean and R. Glowinski Fig.
Page 73 and 74:
62 E.J. Dean and R. Glowinski Assum
Page 75 and 76:
Higher Order Time Stepping for Seco
Page 77 and 78:
u n+1 h Optimal Higher Order Time D
Page 79 and 80:
Optimal Higher Order Time Discretiz
Page 81 and 82:
Optimal Higher Order Time Discretiz
Page 83 and 84: Optimal Higher Order Time Discretiz
Page 103 and 104: 96 I. Sazonov et al. To provide a p
Page 105 and 106: 98 I. Sazonov et al. In the first s
Page 107 and 108: 100 I. Sazonov et al. Fig. 1. An ex
Page 109 and 110: 102 I. Sazonov et al. H z 1 exact F
Page 111 and 112: 104 I. Sazonov et al. (a) (b) Fig.
Page 113 and 114: 106 I. Sazonov et al. Scattering Wi
Page 115 and 116: 108 I. Sazonov et al. 6.4 Scatterin
Page 117 and 118: 110 I. Sazonov et al. (a) (b) Fig.
Page 119 and 120: 112 I. Sazonov et al. [MHP96] K. Mo
Page 121 and 122: 114 R. Sanders and A.M. Tesdall I R
Page 123 and 124: 116 R. Sanders and A.M. Tesdall imp
Page 125 and 126: 118 R. Sanders and A.M. Tesdall alo
Page 127 and 128: 120 R. Sanders and A.M. Tesdall (a)
Page 129 and 130: 122 R. Sanders and A.M. Tesdall D C
Page 131 and 132: 124 R. Sanders and A.M. Tesdall 8.6
Page 133: 126 R. Sanders and A.M. Tesdall 0.3
Page 137 and 138: 132 S. Lapin et al. Ω R γ Ω 2 Γ
Page 139 and 140: 134 S. Lapin et al. ∫ ∂ 2 ∫
Page 141 and 142: 136 S. Lapin et al. Ω R γ Fig. 3.
Page 143 and 144: 138 S. Lapin et al. 4 Energy Inequa
Page 145 and 146: 140 S. Lapin et al. 5 Numerical Exp
Page 147 and 148: 142 S. Lapin et al. Fig. 6. Contour
Page 149 and 150: 144 S. Lapin et al. Fig. 9. Obstacl
Page 151 and 152: Domain Decomposition and Electronic
Page 153 and 154: Domain Decomposition Approach for C
Page 169 and 170: Numerical Analysis of a Finite Elem
Page 181 and 182: so that |u| 2 1,ω h ≤ 2 Numerica
Page 185 and 186:
Numerical Analysis of a Finite Elem
Page 187 and 188:
Numerical Analysis of a Finite Elem
Page 189 and 190:
188 A. Bonito et al. of the model a
Page 191 and 192:
190 A. Bonito et al. Fig. 1. The sp
Page 193 and 194:
192 A. Bonito et al. 3 1 16 4 1 1 1
Page 195 and 196:
194 A. Bonito et al. ∫ v n+1 h
Page 197 and 198:
196 A. Bonito et al. −pn +2µD(v)
Page 199 and 200:
198 A. Bonito et al. each of its pa
Page 201 and 202:
200 A. Bonito et al. The normal vec
Page 203 and 204:
202 A. Bonito et al. with initial c
Page 205 and 206:
204 A. Bonito et al. Fig. 8. Jet bu
Page 207 and 208:
206 A. Bonito et al. References [AM
Page 209 and 210:
208 A. Bonito et al. [Set96] J. A.
Page 211 and 212:
210 J. Hao et al. due to shear flow
Page 213 and 214:
212 J. Hao et al. The backward reac
Page 215 and 216:
214 J. Hao et al. where u and p den
Page 217 and 218:
216 J. Hao et al. * * * * * * * * *
Page 219 and 220:
218 J. Hao et al. and solve for V n
Page 221 and 222:
220 J. Hao et al. Table 2. The calc
Page 223 and 224:
222 J. Hao et al. References [ASS80
Page 225 and 226:
Computing the Eigenvalues of the La
Page 227 and 228:
Eigenvalues of the Laplace-Beltrami
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
A Fixed Domain Approach in Shape Op
Page 235 and 236:
Shape Optimization Problems with Ne
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Reduced-Order Modelling of Dispersi
Page 245 and 246:
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Page 255 and 256:
Calibration of Lévy Processes with
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
We have proved Calibration of Lévy
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Note that p ∗ satisfies Calibrati
Page 273 and 274:
Page 275 and 276:
280 S. Ikonen and J. Toivanen the p
Page 277 and 278:
282 S. Ikonen and J. Toivanen Merto
Page 279 and 280:
284 S. Ikonen and J. Toivanen For H
Page 281 and 282:
286 S. Ikonen and J. Toivanen and {
Page 283 and 284:
288 S. Ikonen and J. Toivanen 1.6 1
Page 285 and 286:
290 S. Ikonen and J. Toivanen 8 Con
Page 287:
292 S. Ikonen and J. Toivanen [Mer7
show all

Partial Differential Equations - Modelling and ... - ResearchGate

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?