This book collects many of the presented papers, as plenary presentations, mini-symposia invited presentations, or contributed talks, from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) 2017. The conference was organized by the University of Bergen, Norway from September 25 to 29, 2017. Leading experts in the field presented the latest results and ideas in the designing, implementation, and analysis of numerical algorithms as well as their applications to relevant, societal problems.ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications. These discussions are upheld at the highest level of international expertise. The first ENUMATH conference was held in Paris in 1995 with successive conferences being held at various locations across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), and Ankara (2015).

Presents innovative research in numerical mathematics Expounds novel applications from leading experts in the fields of numerical analysis and computational mathematics Includes a collection of diverse authors from backgrounds in mathematics and engineering

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Plenary lectures .- PDE Apps for Acoustic Ducts: A Parametrized Component-to-System Model-Order-Reduction Approach.- Sub-voxel perfusion modeling in terms of coupled 3d-1d problem.- Iterative linearisation schemes for doubly degenerate parabolic equations.- Mathematics and Medicine: How mathematics, modelling and simulations can lead to better diagnosis and treatments.- Kernel methods for large scale problems: algorithms and applications .- Convergence of Multilevel Stationary Gaussian Convolution.- Anisotropic weights for RBF-PU interpolation with subdomains of variable shapes.- Radial basis function approximation method for pricing of basket options under jump diffusion model.- Greedy Algorithms for Matrix-Valued Kernels.- GPU Optimization of Large-Scale Eigenvalue Solver.- Advanced discretization methods for computational wave propagation .- On the efficiency of the PeacemanRachford ADI-dG method for wave-type problems.- Trefftz - Discontinuous Galerkin Approach for Solving Elastodynamic Problem.- Unfitted finite element methods: analysis and applications .- FETI-DP preconditioners for the Virtual Element Method on general 2D.- Modeling flow and transport in fractured media by a hybrid finite volume-finite element method.- A cut-cell Hybrid High-Order method for elliptic problems with curved boundaries.- A cut finite element method with boundary value correction for the incompressible Stokes equations.- Numerical Integration on Hyperrectangles in Isoparametric Unfitted Finite Elements.- Advances in numerical linear algebra methods and applications to partial differential equations.- On a generalization of Neumann series of Bessel functions using Hessenberg matrices and matrix exponentials.- Influence of the SIPG penalisation on the numerical properties of linear systems for elastic wave propagation.- Function-based Algebraic Multigrid method for the 3DPoisson problem on structured meshes.- Numerical methods in biophysics .- Mathematical modelling of phenotypic selection within solid tumours.- Uncertainty assessment of a hybrid cell-continuum based model for wound contraction.- Structure preserving discretizations and high order finite elements for differential forms.- The discrete relations between fields and potentials with high order Whitney forms.- Model Order Reduction of an Elastic Body under Large Rigid Motion.- On surface area and length preserving flows of closed curves on a given surface.- Derivation of higher-order terms in FFT-based numerical homogenization.- Monge-Ampère solvers with applications to illumination optics .- A Least-Squares Method for a Monge-Ampère Equation with Non-Quadratic Cost Function Applied to Optical Design.- Solving inverse illumination problems with Liouville's equation.- Mixed and nonsmooth methods in numerical solid mechanics .- Strong vs. Weak Symmetry in Stress-BasedMixed Finite Element Methods for Linear Elasticity.- Evolution of load-bearing structures with phase field modeling.- An accelerated Newton method for nonlinear materials in structure mechanics and fluid mechanics.- A posteriori error estimation, adaptivity and approximation .- Best error localizations for piecewise polynomial approximation of gradients, functions and functionals.- Adaptive Discontinuous Galerkin Methods for flow in porous media.- An adaptive Escheme for conservation laws.- Adaptive Filtered Schemes for first order Hamilton-Jacobi equations.- Goal-oriented a posteriori error estimates in nearly incompressible linear elasticity.- Nitsche's method for the obstacle problem of clamped Kirchhoff plates.- Noncommutative stochastic differential equations: Analysis and simulation.- Stochastic B-series and order conditions for exponential integrators.- What is a post-Lie algebra and why is it useful in geometric integration.- On non-commutative stochastic exponentials.- Innovative numerical methods and their analysis for elliptic and partabolic PDEs .- An introduction to the gradient discretisation method.- Quasi-optimal nonconforming methods for second-order problems on domains with non-Lipschitz boundary.- Convergence of adaptive finite element methods with error-dominated oscillation.- Finite element methods for parabolic problems with time-dependent domains application to a milling simulation.- Polyhedral methods and applications .- Numerical investigation of the conditioning for plane wave discontinuous Galerkin methods.- The Virtual Element Method for the transport of passive scalars in Discrete Fracture Networks.- On the implementation of a multiscale Hybrid High-Order method.- VEM for the Reissner-Mindlin plate based on the MITC approach: the element of degree 2.- Recent advances in space-time Galerkin methods .- DGM for the solution of nonlinear dynamic elasticity.- Higher order space-time elements for a non-linear Biot model.- Iterative Coupling of Mixed and Discontinuous Galerkin Methods for Poroelasticity.- Stability of higher-order ALE-STDGM for nonlinear problems in time-dependent domains.- PDE Software Frameworks .- Implementation of mixed-dimensional models for fractured porous media.- Fast matrix-free evaluation of hybridizable discontinuous Galerkin operators.- Numerical methods for simulating processes in porous media .- Numerical Benchmarking for 3D Multiphase Flow: New Results for a Rising Bubble.- A linear domain decomposition method for two-phase flow in porous media.- A numerical method for an inverse problem arising in two-phase fluid flow transport through a homogeneous porous medium.- A fully-implicit, iterative scheme for the simulation of two-phase flow in porous media.- Mass lumping for MHFEM in two phase flow problems in porous media.- Uncertainty quantification in injection and soil characteristics for Biot's poroelasticity model.- Reactivation of Fractures in Subsurface Reservoirs - a Numerical Approach using a Static-Dynamic Friction Model.- Model reduction methods for simulation and (optimal) control .- POD-Based Economic Model Predictive Control for Heat-Convection Phenomena.- Real-Time Optimization of Thermal Ablation Cancer Treatments.- Parametric model reduction via interpolating orthonormal bases.- A Spectral Element Reduced Basis Method in Parametric CFD.- POD for optimal control of the Cahn-Hilliard system using spatially adapted snapshots.- Recent advances on polyhedral discretizations .- New strategies for the simulation of the flow in three dimensional porofractured media.- The Virtual Element Method on Anisotropic Polygonal Discretizations.- **FEM mes…