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Invited papers.- Discrete Differential Forms, Approximation of
Eigenvalue Problems, and Application to the p Version of Edge
Finite Elements.- Semi-Implicit DGFE Discretization of the
Compressible Navier-Stokes Equations: Efficient Solution Strategy.-
Some Numerical Approaches for Weakly Random Homogenization.- Goal
Oriented, Anisotropic, A Posteriori Error Estimates for the Laplace
Equation.- Contributed papers.- Energy Stability of the MUSCL
Scheme.- Numerical Stabilization of the Melt Front for Laser Beam
Cutting.- Numerical Optimization of a Bioreactor for the Treatment
of Eutrophicated Water.- Finite Element Approximation of a Quasi-3D
Model for Estuarian River Flows.- Convergence of a Mixed
Discontinuous Galerkin and Finite Volume Scheme for the 3
Dimensional Vlasov-Poisson-Fokker-Planck System.- Infrastructure
for the Coupling of Dune Grids.- FEM for Flow and Pollution
Transport in a Street Canyon.- Stabilized Finite Element Methods
with Shock-Capturing for Nonlinear Convection-Diffusion-Reaction
Models.- Finite Element Discretization of the Giesekus Model for
Polymer Flows.- A dG Method for the Strain-Rate Formulation of the
Stokes Problem Related with Nonconforming Finite Element Methods.-
Numerical Simulation of the Stratified Flow Past a Body.- A
Flexible Updating Framework for Preconditioners in PDE-Based Image
Restoration Algorithms.- Stabilized Finite Element Method for
Compressible-Incompressible Diphasic Flows.- An Immersed Interface
Technique for the Numerical Solution of the Heat Equation on a
Moving Domain.- Lid-Driven-Cavity Simulations of Oldroyd-B Models
Using Free-Energy-Dissipative Schemes.- Adaptive Multiresolution
Simulation of Waves in Electrocardiology.- On the Numerical
Approximation of the Laplace Transform Function from Real Samples
and Its Inversion.- A Motion-Aided Ultrasound Image Sequence
Segmentation.- A High Order Finite Volume Numerical Scheme for
Shallow Water System: An Efficient Implementation on GPUs.-
Spectral Analysis for Radial Basis Function Collocation Matrices.-
Finite Element Solution of the Primitive Equations of the Ocean by
the Orthogonal Sub-Scales Method.- Solution of Incompressible Flow
Equations by a High-Order Term-by-Term Stabilized Method.- Solving
Large Sparse Linear Systems Efficiently on Grid Computers Using an
Asynchronous Iterative Method as a Preconditioner.- Hierarchical
High Order Finite Element Approximation Spaces for H(div) and
H(curl).- Some Theoretical Results About Stability for IMEX Schemes
Applied to Hyperbolic Equations with Stiff Reaction Terms.- Stable
Perfectly Matched Layers for the Schroedinger Equations.- Domain
Decomposition Schemes for Frictionless Multibody Contact Problems
of Elasticity.- Analysis and Acceleration of a Fluid-Structure
Interaction Coupling Scheme.- Second Order Numerical Operator
Splitting for 3D Advection-Diffusion-Reaction Models.- Space-Time
DG Method for Nonstationary Convection-Diffusion Problems.- High
Order Finite Volume Schemes for Numerical Solution of Unsteady
Flows.- Multigrid Finite Element Method on Semi-Structured Grids
for the Poroelasticity Problem.- A Posteriori Error Bounds for
Discontinuous Galerkin Methods for Quasilinear Parabolic Problems.-
An A Posteriori Analysis of Multiscale Operator Decomposition.-
Goal-Oriented Error Estimation for the Discontinuous Galerkin
Method Applied to the Biharmonic Equation.- Solving Stochastic
Collocation Systems with Algebraic Multigrid.- Adaptive Two-Step
Peer Methods for Incompressible Navier-Stokes Equations.- On
Hierarchical Error Estimators for Time-Discretized Phase Field
Models.- Nonlinear Decomposition Methods in Elastodynamics.- An
Implementation Framework for Solving High-Dimensional PDEs on
Massively Parallel Computers.- Benchmarking FE-Methods for the
Brinkman Problem.- Finite Element Based Second Moment Analysis for
Elliptic Problems in Stochastic Domains.- On Robust Parallel
Preconditioning for Incompressible Flow Problems.- Hybrid Modeling
of Plasmas.- A Pr
The European Conference on Numerical Mathematics and Advanced
Applications (ENUMATH) was held from June 29-July 3, 2010, in
Uppsala, Sweden. This was the eighth conference in a series of
biannual meetings starting in Paris (1995). S- sequent conferences
were organized in Heidelberg (1997), Jyvas ] kyla ] (1999), Ischia
(2001), Prague (2003), Santiago de Compostela (2005), and Graz
(2007). ENU- MATH 2009 attracted over 330 attendees to the scienti
c programme, with ten invited speakers, one public lecture, 32
minisymposia, and more than 280 presen- tions. This volume contains
a selection of papers by the invited speakers and from the
minisymposia and the contributed sessions. The purpose of the
conference was to create a forum for discussion and d- semination
of recent results in numerical mathematics and new applications of
computational methods. Many subjects were covered in the talks and
a few of the topicsrepresentedin these proceedingswere
discontinuousGalerkinmethods, nite
elementmethodsindifferentapplications, methodsfor uid ow,
electromagnetism, nancial engineering, structuralmechanics,
optimalcontrol, andbiomechanics. The minisymposia listed below with
their organizers also give an impression of how broad the scope of
the conference was: Adaptivity for non-linearand non-smooth
problems, part I & II, Ralf Kornhuber, Andreas Veeser Advanced
techniques in radial basis function approximation for PDEs, partI
& II, Natasha Flyer, Elisabeth Larsson Advances in numerical
methods for non-Newtonian ?ows, part I & II, Erik Burman, Maxim
Olshanskii, Stefan Turek Anisotropicadaptivemeshes:
erroranalysisandapplications, partI&II, Thierry Coupez, Simona
Perotto Asymptotic linear algebra, numerical methods, and
applications, part I & II, Marco Donatelli, Stefano
Serra-Capizzano Biomechanics, part I & II, Gerhard A."
Multiscale problems naturally pose severe challenges for
computational science and engineering. The smaller scales must be
well resolved over the range of the larger scales. Challenging
multiscale problems are very common and are found in e.g. materials
science, fluid mechanics, electrical and mechanical engineering.
Homogenization, subgrid modelling, heterogeneous multiscale
methods, multigrid, multipole, and adaptive algorithms are examples
of methods to tackle these problems. This volume is an overview of
current mathematical and computational methods for problems with
multiple scales with applications in chemistry, physics and
engineering.
Most problems in science involve many scales in time and space. An
example is turbulent ?ow where the important large scale quantities
of lift and drag of a wing depend on the behavior of the small
vortices in the boundarylayer. Another example is chemical
reactions with concentrations of the species varying over seconds
and hours while the time scale of the oscillations of the chemical
bonds is of the order of femtoseconds. A third example from
structural mechanics is the stress and strain in a solid beam which
is well described by macroscopic equations but at the tip of a
crack modeling details on a microscale are needed. A common
dif?culty with the simulation of these problems and many others in
physics, chemistry and biology is that an attempt to represent all
scales will lead to an enormous computational problem with
unacceptably long computation times and large memory requirements.
On the other hand, if the discretization at a coarse level
ignoresthe?nescale
informationthenthesolutionwillnotbephysicallymeaningful. The
in?uence of the ?ne scales must be incorporated into the model.
This volume is the result of a Summer School on Multiscale Modeling
and S- ulation in Science held at Boso n, Lidingo outside
Stockholm, Sweden, in June 2007. Sixty PhD students from applied
mathematics, the sciences and engineering parti- pated in the
summer school."
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