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On minimax cardinal spline interpolation
It is shown that in the problem of cardinal interpolation, spline interpolants of various degrees are R -minimax, with respect to corresponding...
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Local Wavelet Adaptation of Cartesian Grids in Computational Fluid Dynamics
AbstractA method for dynamic local adaptation of graded Cartesian trees for the numerical solution of fluid dynamics problems is presented. Local...
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Analogs of the Riesz Identity, and Sharp Inequalities for Derivatives and Differences of Splines in the Integral Metric
An analog of the Riesz interpolation formula is established. It allows us to obtain a sharp estimate for the first order derivative of a spline of...
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Analog of the Riesz Identity and Sharp Inequalities for Derivatives and Differences of Splines in the Uniform Metric
We establish an analog of the Riesz interpolation formula owing to which it is possible to obtain a sharp estimate for the first order derivative of...
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Sharp Kolmogorov–Remez-Type Inequalities for Periodic Functions of Low Smoothness
In the case where either r = 2, k = 1 or r = 3, k = 1, 2, for any q , p ≥ 1, β ∈ [0, 2π), and a Lebesgue-measurable set B ⊂ I 2π ≔ [−π/2, 3π/2], μB ≤ β ,...
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Clothoid fitting and geometric Hermite subdivision
We consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector...
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Historical steps of development of convexity as a field
In this chapter we will show historical steps of the development of convexity as a field and, in addition, developments of the relations between...
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Deferred Correction Methods for Ordinary Differential Equations
Deferred correction is a well-established method for incrementally increasing the order of accuracy of a numerical solution to a set of ordinary...
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Direct Flow Simulation of Objects Represented by Point Clouds
In this chapter, we present a recently proposed approach for performing multiphysics analysis using immersogeometric analysis (IMGA) on complex...
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Applications of time parallelization
This review article serves to summarize the many advances in time-parallel computations since the excellent review article by Gander, “50 years of...
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A retrospective on research visits of Paul Butzer’s Aachen research group to Eastern Europe and Tenerife
Our article “A retrospective on research visits of Paul Butzer’s Aachen research group to North America and Western Europe” [
1 ] concerned the... -
Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element Methods
We build a multi-element variant of the smoothness increasing accuracy conserving (SIAC) shock capturing technique proposed for single element...
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Template-Based Image Reconstruction Facing Different Topologies
The reconstruction of images from measured data is an increasing field of research. For highly under-determined problems, template-based image...
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On Robust and Adaptive Finite Volume Methods for Steady Euler Equations
In this paper, a robust and adaptive framework of finite volume solutions for steady Euler equations is introduced. On a given mesh, the numerical...
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Topology Optimization in Linear Elasticity, Plasticity and Fracture Mechanics
This chapter presents the theoretical and the numerical study of shape and topology optimization for linear elasticity, plasticity and fracture using...
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The PDD Method for Solving Linear, Nonlinear, and Fractional PDEs Problems
We review the Probabilistic Domain Decomposition (PDD) method for the numerical solution of linear and nonlinear Partial Differential Equation (PDE)...
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Numerical Integration of Partial Differential Equations
A very large range of efficient techniques are exposed for solving partial differential equations. Various physical systems illustrate the different...
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Decision, Planning, and Control
In this chapter, we continue with our general discussion of the planning and control modules by expanding on the concepts of behavior decision,...
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Asymptotic Properties of Chebyshev Splines with Fixed Number of Knots
V. M. Tikhomirov expressed Kolmogorov widths of the class W r := W
∞ r [−1, 1] in the space C := C [ − 1 , 1] as a norm of special splines: d ...