Numerical Mathematics and Advanced Applications (eBook)

Preface 5
Contents 7
Plenary Lectures 16
The Worst Scenario Method: A Red Thread Running Through Various Approaches to Problems with Uncertain Input Data 17
Boundary and Finite Element Domain Decomposition Methods 29
Discontinuous Galerkin Elements for Reissner- Mindlin Plates 41
Contributed Lectures 51
A Posteriori Error Estimation and Adaptive Methods 52
Functional Type A Posteriori Error Estimates for Maxwell’s Equations 53
Space–Time Adaption for Advection- Diffusion- Reaction Problems on Anisotropic Meshes 61
A Posteriori Error Analysis for Kirchhoff Plate Elements 69
Adaptive Finite Element Simulation of Relaxed Models for Liquid- Solid Phase Transition 77
Biomedical Applications 85
A Numerical Study of the Interaction of Blood Flow and Drug Release from Cardiovascular Stents 86
Numerical Modelling of Epidermal Wound Healing 94
Model of Multiple Lexicographical Programming Applied in Cervical Cancer Screening 102
A Finite Element Model for Bone Ingrowth into a Prosthesis 110
Computational Electromagnetism 118
Space and Time Adaptive Calculation of Transient 3D Magnetic Fields 119
A Boundary Integral Formulation for Nonlocal Electrostatics 127
Computational Methods, Preconditioners, Solvers 135
Efficient Solution of Algebraic Bernoulli Equations Using H -Matrix Arithmetic 136
A Purely Algebraic Approach to Preconditioning Based on Hierarchical LU Factorizations 144
Additive Schwarz Preconditioners for Degenerate Problems with Isotropic Coefficients 152
Performance Analysis of Parallel Algebraic Preconditioners for Solving the RANS Equations Using Fluctuation Splitting Schemes 160
On Least-Squares Approximate Inverse-Based Preconditioners 168
On the Construction of Stable B-Spline Wavelet Bases 176
The Performance of a Multigrid Algorithm for the Acoustic Single Layer Equation 184
Constraints Coefficients in hp-FEM 192
A Boundary Element Algorithm for the Dirichlet Eigenvalue Problem of the Laplace Operator 200
On Efficient Solution of Linear Systems Arisingin hp-FEM 208
Convection, Diffusion, Conservation, and Hyperbolic Systems 216
Coupling Two Scalar Conservation Laws via Dafermos’ Self- Similar Regularization 217
A Sharp Interface and Fully Conservative Scheme for Computing Nonclassical Shocks 225
A Numerical Descent Method for an Inverse Problem of a Scalar Conservation Law Modelling Sedimentation 233
PSI Solution of Convection-Diffusion Equationswith Data in L 241
High Order Two Dimensional Numerical Schemes for the Coupling of Transport Equations and ShallowWater Equations 249
Well-Balanced High-Order MUSTA Schemes for Non- Conservative Hyperbolic Systems 257
Local Time Stepping for Implicit-Explicit Methods on Time Varying Grids 265
A ‘TVD-like’ Scheme for Conservation Laws with Source Terms 273
Application of the WAF Method to Shallow Water Equations with Pollutant and Non- Constant Bottom 281
A Third Order Method for Convection-Diffusion Equations with a Delay Term 289
A Third Order WLSQR Scheme on Unstructured Meshes with Curvilinear Boundaries 297
On the Choice of Parameters in Stabilization Methods for Convection– Diffusion Equations 305
On Path-Conservative Numerical Schemes for Hyperbolic Systems of Balance Laws 313
Discontinuous Galerkin Methods 321
An Augmented DG Scheme for Porous Media Equations 322
A Remark to the DGFEM for Nonlinear Convection- Diffusion Problems Applied on Nonconforming Meshes 330
BDF-DGFE Method for the Compressible Navier- Stokes Equations 338
Discontinuous Galerkin Method for the Numerical Solution of Inviscid and Viscous Compressible Flow 346
Numerical Integration in the Discontinuous Galerkin Method for Nonlinear Convection- Diffusion Problems in 3D 354
Implicit-Explicit Runge-Kutta Discontinuous Galerkin Finite Element Method for Convection- Diffusion Problems 362
Domain Decomposition Methods 370
A Domain Decomposition Method Derived from the Primal Hybrid Formulation for 2nd Order Elliptic Problems 371
A Posteriori Error Analysis of Penalty Domain Decomposition Methods for Linear Elliptic Problems 379
BETI-DP Methods in Unbounded Domains 387
Domain Decomposition and Model Reduction of Systems with Local Nonlinearities 395
An Adaptive Discontinuous Galerkin Scheme for Second Order Problems with an Interface 403
Finance, Stochastic Applications 411
Abstract Sensitivity Analysis for Nonlinear Equations and Applications 412
Multiscale Analysis for Jump Processes in Finance 420
Fluid Mechanics 428
A Hybrid Numerical Scheme for Aerosol Dynamics 429
Numerical Study of Mixed Finite Element and Multi Point Flux Approximation of Flow in Porous Media 437
Local Projection Stabilization for the Oseen System on Anisotropic Cartesian Meshes 445
Simulations of 3D Dynamics of Microdroplets: A Comparison of Rectangular and Cylindrical Channels 453
Incomplete Interior Penalty Galerkin Method for a Nonlinear Convection- Diffusion Equation 461
Numerical Simulations of Incompressible Laminar Flow for Newtonian and Non- Newtonian Fluids 469
Numerical Solution of 2D and 3D Unsteady Viscous Flows 477
Local Projection Stabilization of Finite Element Methods for Incompressible Flows 485
A Numerical Study of Local Projection Stabilisations Applied to Oseen Problems 493
Involutive Completion to Avoid LBB Condition 501
Numerical Computation of Unsteady Compressible Flows with Very Low Mach Numbers 509
A Mixed Hybrid Finite Element Discretization Scheme for Reactive Transport in Porous Media 517
Applying Local Projection Stabilization to inf- sup Stable Elements 525
Calibration of Model and Discretization Parameters for Turbulent Channel Flow 533
Fluid-Structure Interaction 541
Numerical Solution of Transonic and Supersonic 2D and 3D Fluid– Elastic Structure Interaction Problems 542
Numerical Simulations of Flow Induced Vibrations of a Profile 550
A Semi-Implicit Algorithm Based on the Augmented Lagrangian Method for Fluid- Structure Interaction 558
Automated Multi-Level Substructuring for a Fluid- Solid Vibration Problem 566
On Numerical Approximation of Fluid- Structure Interaction Problems 574
Optimal Control Problems 582
Fishways Design: An Application of the Optimal Control Theory 583
Moving Domain by Galerkin-Level Set Strategy: Application to Shape Geodesics 591
Numerical Analysis of a Control and State Constrained Elliptic Control Problem with Piecewise Constant Control Approximations 599
Globalization of Nonsmooth Newton Methods for Optimal Control Problems 607
An Inexact Trust-Region SQP Method with Applications to PDE- Constrained Optimization 615
Semi–Monotonic Augmented Lagrangians for Optimal Control and Parameter Identification 623
An Optimal Control Problem for Stochastic Linear PDE’s Driven by a Gaussian White Noise 631
A Priori Error Analysis for the Finite Element Approximation of Elliptic Dirichlet Boundary Control Problems 639
A Priori Error Analysis for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems 647
Multigrid Methods for Linear Elliptic Optimal Control Problems 655
Optimization, Inverse Problems 663
An Active Curve Approach for Tomographic Reconstruction of Binary Radially Symmetric Objects 664
A Single-Pass Scheme for the Mean Curvature Motion of Convex Curves 672
A Semi-Lagrangian Approximation of Min– Max Type for the Stationary Mean Curvature Equation 680
Topological Derivative Based Methods for Non– Destructive Testing 688
A Characteristics Driven Fast Marching Method for the Eikonal Equation 696
Hierarchical Model Reduction for Advection- Diffusion- Reaction Problems 704
A Semi-Lagrangian Scheme for the Open Table Problem in Granular Matter Theory 712
On a Variational Approximation of the Effective Hamiltonian 720
Estimation of Diffusion Coefficients in a Scalar Ginzburg- Landau Equation by Using Model Reduction 728
Reduced Order Models (POD) for Calibration Problems in Finance 736
Ordinary Differential Equations 744
A Collocation Method for Quadratic Control Problems Governed by Ordinary Elliptic Differential Equations 745
A Road Traffic Model with Overtaking: Continuation of the Oscillatory Patterns 753
A Second Order Scheme for Solving Optimization- Constrained Differential Equations with Discontinuities 761
Optimal Load Changes for a Molten Carbonate Fuel Cell Model 769
Differential DAE Index for Reactive Euler Equations 777
Application of a First Order Asymptotic Method for Modeling Singularly Perturbed BVPs 785
Solid Mechanics 793
Newton-Like Solver for Elastoplastic Problems with Hardening and its Local Super- Linear Convergence 794
On a Fictitious Domain Method for Unilateral Problems 802
Bifurcations in Contact Problems with Local Coulomb Friction 810
Point Load on a Shell 818