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Electromagnetic Scattering 111 proved to be less sensitive to special geometric features, such as singularities and regions of high curvature. It is anticipated that, for three-dimensional problems, a speed-up factor of three orders of magnitude could be achieved, if the mesh generation method can be extended to provide high quality tetrahedral elements. References [Ber94] J.-P. Berenger. A perfectly matched layer for absorption of electromagnetic waves. J. Comput. Phys., 114:185–200, 1994. [BP97] F. Bonnet and F. Poupaud. Berenger absorbing boundary condition with time finite-volume scheme for triangular meshes. Appl. Numer. Math., 25:333–354, 1997. [CFS93] J. P. Cioni, L. Fezoui, and H. Steve. A parallel time-domain Maxwell solver using upwind schemes and triangular meshes. Impact Comput. Sci. Engrg., 5:215–247, 1993. [DBB99] A. Deraemaeker, I. Babuška, and P. Bouillard. Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. Internat. J. Numer. Methods Engrg., 46:471–499, 1999. [DH03] J. Donéa and A. Huerta. Finite element methods for flow problems. John Wiley & Sons, 2003. [DL97] E. Darve and R. Löhner. Advanced structured-unstructured solver for electromagnetic scattering from multimaterial objects. AIAA Paper 97–0863, Washington, 1997. [EHM + 03] M. El hachemi, O. Hassan, K. Morgan, D. P. Rowse, and N. P. Weatherill. Hybrid methods for electromagnetic scattering simulations on overlapping grids. Comm. Numer. Methods Engrg., 19:749–760, 2003. [EL02] F. Edelvik and G. Ledfelt. A comparison of time-domain hybrid solvers for complex scattering problems. Internat. J. Numer. Model.: Elect. Net. Dev. Fields, 15:475–487, 2002. [Geo91] P. L. George. Automatic mesh generation. Applications to finite element methods. John Wiley & Sons, 1991. [GL93] S. Gedney and F. Lansing. Full wave analysis of printed microstrip devices using a generalized Yee algorithm. In Proceedings of the IEEE Antenas and Propagation Society International Symposium, pages 1179–1182, Ann Arbor, 1993. Pennsylvania State University. [LMHW02] P. D. Ledger, K. Morgan, O. Hassan, and N. P. Weatherill. Arbitrary order edge elements for electromagnetic scattering simulations using hybrid meshes and a PML. Internat. J. Numer. Methods Engrg., 55:339–358, 2002. [Mad95] N. Madsen. Divergence preserving discrete surface integral methods for Maxwell’s equations using nonorthogonal unstructured grids. J. Comput. Phys., 119:35–45, 1995. [MHP94] K. Morgan, O. Hassan, and J. Peraire. An unstructured grid algorithm for the solution of Maxwell’s equations in the time domain. Internat. J. Numer. Methods Fluids, 19:849–863, 1994.
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Partial Differential Equations
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Partial Differential Equations Mode
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Dedicated to Olivier Pironneau
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VIII Preface computers has been at
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Contents List of Contributors .....
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List of Contributors Yves Achdou UF
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List of Contributors XV Claude Le B
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Discontinuous Galerkin Methods Vive
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Discontinuous Galerkin Methods 5 2
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Discontinuous Galerkin Methods 7 g
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Discontinuous Galerkin Methods 9 (
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Discontinuous Galerkin Methods 15 W
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Let a h and b h denote the bilinear
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Discontinuous Galerkin Methods 19 t
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Discontinuous Galerkin Methods 21 l
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Table 1. Primal DG for transport Di
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Discontinuous Galerkin Methods 25 [
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Mixed Finite Element Methods on Pol
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Mixed FE Methods on Polyhedral Mesh
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4 Hybridization and Condensation Mi
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is symmetric and positive definite,
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with some coefficient α ∈ R wher
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44 E.J. Dean and R. Glowinski so fa
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46 E.J. Dean and R. Glowinski 2 A L
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48 E.J. Dean and R. Glowinski S:T=
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50 E.J. Dean and R. Glowinski minim
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52 E.J. Dean and R. Glowinski 6 On
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54 E.J. Dean and R. Glowinski Fig.
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Numerical Analysis of a Finite Elem
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so that |u| 2 1,ω h ≤ 2 Numerica
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188 A. Bonito et al. of the model a
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190 A. Bonito et al. Fig. 1. The sp
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192 A. Bonito et al. 3 1 16 4 1 1 1
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194 A. Bonito et al. ∫ v n+1 h
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196 A. Bonito et al. −pn +2µD(v)
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198 A. Bonito et al. each of its pa
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200 A. Bonito et al. The normal vec
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202 A. Bonito et al. with initial c
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204 A. Bonito et al. Fig. 8. Jet bu
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206 A. Bonito et al. References [AM
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208 A. Bonito et al. [Set96] J. A.
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210 J. Hao et al. due to shear flow
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212 J. Hao et al. The backward reac
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214 J. Hao et al. where u and p den
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216 J. Hao et al. * * * * * * * * *
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218 J. Hao et al. and solve for V n
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220 J. Hao et al. Table 2. The calc
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222 J. Hao et al. References [ASS80
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Computing the Eigenvalues of the La
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Eigenvalues of the Laplace-Beltrami
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A Fixed Domain Approach in Shape Op
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Shape Optimization Problems with Ne
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Reduced-Order Modelling of Dispersi
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Calibration of Lévy Processes with
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We have proved Calibration of Lévy
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Note that p ∗ satisfies Calibrati
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280 S. Ikonen and J. Toivanen the p
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282 S. Ikonen and J. Toivanen Merto
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284 S. Ikonen and J. Toivanen For H
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286 S. Ikonen and J. Toivanen and {
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288 S. Ikonen and J. Toivanen 1.6 1
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290 S. Ikonen and J. Toivanen 8 Con
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