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Testimonies
We contacted several researchers who worked on the topics treated in this book or related to them, and asked them for their testimony about the...
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Optimal control for estimation in partially observed elliptic and hypoelliptic linear stochastic differential equations
Multi-dimensional stochastic differential equations (SDEs) are a powerful tool to describe dynamics of phenomena that change over time. We focus on...
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A Bivariate Spline Method for Second Order Elliptic Equations in Non-divergence Form
A bivariate spline method is developed to numerically solve second order elliptic partial differential equations in non-divergence form. The...
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Suitable Spaces for Shape Optimization
The differential-geometric structure of the manifold of smooth shapes is applied to the theory of shape optimization problems. In particular, a...
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Approximation Properties of the Sampling Kantorovich Operators: Regularization, Saturation, Inverse Results and Favard Classes in \(L^p\)-Spaces
In the present paper, a characterization of the Favard classes for the sampling Kantorovich operators based upon bandlimited kernels has been...
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Direct Acoustic Obstacle Scattering
This chapter is devoted to the solution of the direct obstacle scattering problem for acoustic waves.
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Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier–Stokes equations
Inf-sup stable FEM applied to time-dependent incompressible Navier–Stokes flows are considered. The focus lies on robust estimates for the kinetic...
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A Geometric Framework for Stochastic Shape Analysis
We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types descends to stochastic evolution of shapes, images and...
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Variational integrators for orbital problems using frequency estimation
In this work, we present a new derivation of higher order variational integration methods that exploit the phase lag properties for numerical...
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Multi-objective Geometry Optimization of a Gas Cyclone Using Triple-Fidelity Co-Kriging Surrogate Models
Cyclone separators are widely used in a variety of industrial applications. A low-mass loading gas cyclone is characterized by two performance...
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A Review on Variable-Order Fractional Differential Equations: Mathematical Foundations, Physical Models, Numerical Methods and Applications
Variable-order (VO) fractional differential equations (FDEs) with a time ( t ), space ( x ) or other variables dependent order have been successfully...
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Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story?
The contents of this paper is twofold. First, important recent results concerning finite element methods for convection-dominated problems and...
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Computer Graphics
This chapter introduces the applications of computational conformal geometry on computer graphics research. Specifically we focus on digital geometry...
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Functions and their derivatives
In very generalized terms, a real function y = f(x) can be understood as a rule for assigning a real number y to a real number x. Some functions play...
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Interpolation and Approximation
This chapter begins with a discussion of interpolation. Polynomial interpolation for a function of a single variable is analyzed, and implemented...
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Heat and Wave Equations
We introduce the heat (Sec. 2.1) and wave (Sec. 2.2) equations; then, we discuss their discretization (Sec. 2.3), the selection of the time scale,...
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Funktionen und Grenzwerte
Zusammenhänge zwischen mathematischen oder technisch-physikalischen Größen werden durch Funktionen beschrieben.
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High Resolution Finite Volume Scheme Based on the Quintic Spline Reconstruction on Non-uniform Grids
This paper presents a compact quintic spline reconstruction for finite volume method on non-uniform structured grids. The primitive function of a...
