Boris Korneev, Vadim Levchenko,
Tópico(s): Gas Dynamics and Kinetic Theory
2016 - Pleiades Publishing | Computational Mathematics and Mathematical Physics
C Bertoglio, Boris N. Khoromskij,
Tensor-product approximation provides a convenient tool for efficient numerical treatment of high-dimensional problems that arise, in particular, in electronic structure calculations in Rd. In this work we apply tensor approximation to the Galerkin representation of the Newton and Yukawa potentials for a set of tensor-product, piecewise polynomial basis functions. To construct tensor-structured representations, we make use of the well-known Gaussian transform of the potentials, and then approximate ...
Tópico(s): Electromagnetic Scattering and Analysis
2011 - Elsevier BV | Computer Physics Communications
Dmitriy Leykekhman, Boris Vexler,
The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the time discontinuous Galerkin solution of linear parabolic equations. Such estimates have many applications. They are essential, for example, in establishing optimal a priori error estimates in non-Hilbertian norms without unnatural coupling of spatial mesh sizes with time steps.
Tópico(s): Numerical methods in engineering
2016 - Springer Science+Business Media | Numerische Mathematik
Angelos Mantzaflaris, Bert Jüttler, Boris N. Khoromskij, Ulrich Langer,
Tópico(s): Polynomial and algebraic computation
2016 - Elsevier BV | Computer Methods in Applied Mechanics and Engineering
Boris Jalušić, Jurica Sorić, Tomislav Jarak,
Tópico(s): Rock Mechanics and Modeling
2016 - Springer Science+Business Media | Computational Mechanics
Dominik Meidner, Boris Vexler,
We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0) in time (which is a variant of the implicit Euler scheme) and with conforming finite elements in space. The main contribution of this paper is the proof of the uniform boundedness of the discrete solution. This allows us to obtain optimal error estimates with respect to various norms.
Tópico(s): Advanced Numerical Methods in Computational Mathematics
2018 - EDP Sciences | ESAIM Mathematical Modelling and Numerical Analysis
Boris N. Khoromskij, Christoph Schwab,
We investigate the convergence rate of approximations by finite sums of rank-1 tensors of solutions of multiparametric elliptic PDEs. Such PDEs arise, for example, in the parametric, deterministic reformulation of elliptic PDEs with random field inputs, based, for example, on the M-term truncated Karhunen–Loève expansion. Our approach could be regarded as either a class of compressed approximations of these solutions or as a new class of iterative elliptic problem solvers for high-dimensional, parametric, ...
Tópico(s): Advanced Numerical Methods in Computational Mathematics
2011 - Society for Industrial and Applied Mathematics | SIAM Journal on Scientific Computing
Reza Abedi, Boris Petracovici, Robert B. Haber,
We present a new space–time discontinuous Galerkin finite element method for linearized elastodynamics that delivers exact balance of linear and angular momentum over every space–time element. The method is formulated for use with fully unstructured space–time grids and uses displacement basis functions that are discontinuous across all inter-element boundaries. We introduce a new space–time formulation of continuum elastodynamics that uses differential forms and the exterior calculus on manifolds ...
Tópico(s): Model Reduction and Neural Networks
2005 - Elsevier BV | Computer Methods in Applied Mechanics and Engineering
Dmitriy Leykekhman, Boris Vexler,
In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty$ norm. The discretization method uses continuous Lagrange finite elements in space and discontinuous Galerkin methods in time of an arbitrary order. The method of proof differs from the established fully discrete error estimate techniques and for the first time allows one to obtain such results in ...
Tópico(s): Differential Equations and Numerical Methods
2016 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
Boris Bonev, Jan S. Hesthaven, Francis X. Giraldo, Michal A. Kopera,
We present a novel high-order discontinuous Galerkin discretization for the spherical shallow water equations, able to handle wetting/drying and non-conforming, curved meshes in a well-balanced manner. This requires a well-balanced discretization, that cannot rely on exact quadrature, due to the curved mesh. Using the strong form of the discontinuous Galerkin discretization, we achieve a splitting of the well-balanced condition into individual problems for the flux and volume terms, which has significant ...
Tópico(s): Navier-Stokes equation solutions
2018 - Elsevier BV | Journal of Computational Physics
Dominik Meidner, Boris Vexler,
In this paper, a finite element discretization of an optimal control problem governed by the heat equation is considered. The temporal discretization is based on a Petrov–Galerkin variant of the Crank–Nicolson scheme, whereas the spatial discretization employs usual conforming finite elements. With a suitable postprocessing step, a discrete solution is obtained for which error estimates of optimal order are proven. A numerical result is presented for illustrating the theoretical findings.
Tópico(s): Advanced Mathematical Modeling in Engineering
2011 - Society for Industrial and Applied Mathematics | SIAM Journal on Control and Optimization
Thomas Richter, Andreas Springer, Boris Vexler,
Tópico(s): Advanced Mathematical Modeling in Engineering
2012 - Springer Science+Business Media | Numerische Mathematik
Tomislav Jarak, Boris Jalušić, Jurica Sorić,
The paper presents meshless methods based on the mixed Meshless Local Petrov-Galerkin approach used for solving linear fourth-order differential equations.In all the methods presented here, the primary variable and its derivatives up to the third order are approximated separately.Three different mixed meshless methods are derived by different choices of test and trial functions and are verified using available analytical and reference solutions.The numerical performance of the presented algorithms ...
Tópico(s): Electromagnetic Simulation and Numerical Methods
2020 - | Transactions of FAMENA
Ragnar Lehmann, Mária Lukáčová-Medviďová, Boris Kaus, Anton Popov,
We describe a Discontinuous Galerkin (DG) scheme for variable‐viscosity Stokes flow which is a crucial aspect of many geophysical modelling applications and conduct numerical experiments with different elements comparing the DG approach to the standard Finite Element Method (FEM). We compare the divergence‐conforming lowest‐order Raviart‐Thomas (RT 0 P 0 ) and Brezzi‐Douglas‐Marini (BDM 1 P 0 ) element in the DG scheme with the bilinear Q 1 P 0 and biquadratic Q 2 P 1 elements for velocity and their matching ...
Tópico(s): Lattice Boltzmann Simulation Studies
2015 - Wiley | ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Dmitriy Leykekhman, Boris Vexler,
The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the lowest order time discontinuous Galerkin solution of linear parabolic equations with time-dependent coefficients. Such estimates have many applications. As one of the applications we establish best approximations type results with respect to the $L^p(0,T;L^2(\Omega))$ norm for $1\le p\le \infty$.
Tópico(s): Stability and Controllability of Differential Equations
2018 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
... captured. We show that when the generalized Taylor Galerkin finite element model is combined with the flux corrected transport technique of Boris and Book, the acoustic field can be more ...
Tópico(s): Ultrasonics and Acoustic Wave Propagation
1994 - World Scientific | Journal of Computational Acoustics
Dmitriy Leykekhman, Boris Vexler,
In this paper we establish best approximation property of fully discrete Galerkin solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty(I;W^{1,\infty}(\Om))$ norm. The discretization method consists of continuous Lagrange finite elements in space and discontinuous Galerkin methods of arbitrary order in time. The method of the proof differs from the established fully discrete error estimate techniques and uses only elliptic results and discrete maximal ...
Tópico(s): Differential Equations and Numerical Methods
2017 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
Wolfgang Hackbusch, Boris N. Khoromskij, Stefan Sauter,
In this paper, we will propose a boundary element method for solving classical boundary integral equations on complicated surfaces which, possibly, contain a large number of geometric details or even uncertainties in the given data. The (small) size of such details is characterised by a small parameter $$\varepsilon$$ and the regularity of the solution is expected to be low in such zones on the surface (which we call the wire-basket zones). We will propose the construction of an initial discretisation ...
Tópico(s): Electromagnetic Simulation and Numerical Methods
2006 - Springer Science+Business Media | Numerische Mathematik
Wendell Mills, Boris Weisfeiler, Allan M. Krall,
... and partial differential equations and eigenvalue problems using Galerkin—projective—finite element techniques.Boris WeisfeilerBoris Weisfeiler received his M.S. from the ...
Tópico(s): Computability, Logic, AI Algorithms
1979 - Taylor & Francis | American Mathematical Monthly
... since 1958 until 2017) was established by academic Boris G. Galerkin. Galerkin had excellent contacts to German scientists, among ...
Tópico(s): History and Theory of Mathematics
2020 - Wiley | ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Dmitriy Leykekhman, Boris Vexler,
Tópico(s): Computational Fluid Dynamics and Aerodynamics
2023 - Springer Science+Business Media | CALCOLO
N. A. Zaitsev, Boris Viktorovich Kritskiy,
О р д е н а Л е н и н а ИНСТИТУТ ПРИКЛАДНОЙ МАТЕМАТИКИ имени М.В.Келдыша Р о с с и й с к о й а к а д е м и и н а у к Н. А. Зайцев, Б. В. Критский Расчет течений жидкости Ван дер Ваальса в модели диффузного интерфейса локальным разрывным методом Галеркина Москва -2018 Н. А. Зайцев, Б. В. Критский.Расчет течений жидкости Ван дер Ваальса в модели диффузного интерфейса локальным разрывным методом Галеркина.Аннотация.В препринте описывается математическая постановка задачи двухфазного однокомпонентного ...
Tópico(s): Gas Dynamics and Kinetic Theory
2018 - | Keldysh Institute Preprints
Boris Korneev, Andrey Zakirov, Vadim Levchenko,
Abstract In this paper, a numerical scheme for solving the equations of the dynamics of a compressible fluid, based on the Runge–Kutta discontinuous Galerkin (RKDG) method and an adaptively refined cubic mesh (AMR), is applied to the problems of shock interaction with solid and liquid obstacles. Features of effective implementation algorithm for the graphic processors (GPU) are described. Several well-known validation test problems are considered. Results of full detailed three-dimensional simulations ...
Tópico(s): Gas Dynamics and Kinetic Theory
2021 - IOP Publishing | Journal of Physics Conference Series
Paul Houston, Sarah Roggendorf, Kristoffer G. van der Zee,
In this article we consider the numerical approximation of the convection-diffusion-reaction equation. One of the main challenges of designing a numerical method for this problem is that boundary layers occurring in the convection-dominated case can lead to non-physical oscillations in the numerical approximation, often referred to as Gibbs phenomena. The idea of this article is to consider the approximation problem as a residual minimization in dual norms in Lq-type Sobolev spaces, with 1<q<∞. We ...
Tópico(s): Numerical methods in inverse problems
2020 - Elsevier BV | Computers & Mathematics with Applications
Boris Jalušić, Tomislav Jarak, Jurica Sorić,
Tópico(s): Composite Structure Analysis and Optimization
2020 - Springer Science+Business Media | Computational Mechanics
Bärbel Holm, Thomas P. Wihler,
We consider continuous and discontinuous Galerkin time stepping methods of arbitrary order as applied to first-order initial value ordinary differential equation problems in real Hilbert spaces. Our only assumption is that the nonlinearities are continuous; in particular, we include the case of unbounded nonlinear operators. Specifically, we develop new techniques to prove general Peano-type existence results for discrete solutions. In particular, our results show that the existence of solutions ...
Tópico(s): Differential Equations and Numerical Methods
2017 - Springer Science+Business Media | Numerische Mathematik
Dominik Schötzau, Ch. Schwab, Thomas P. Wihler,
We introduce and analyze $hp$-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away ...
Tópico(s): Advanced Mathematical Modeling in Engineering
2013 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
James H. Bramble, Stephen Hilbert,
... Previous article Next article FiguresRelatedReferencesCited ByDetails An Interpolated Galerkin Finite Element Method for the Poisson EquationJournal of ... 4 | 26 Nov 2021 Cross Ref A Weak Galerkin Harmonic Finite Element Method for Laplace EquationCommunications on ... Ref A unified study on superconvergence analysis of Galerkin FEM for singularly perturbed systems of multiscale natureJournal ... Ref Integration by interpolation and look-up for Galerkin-based isogeometric analysisComputer Methods in Applied Mechanics and ...
Tópico(s): Mathematical functions and polynomials
1970 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
Scott Congreve, Paul Houston, Thomas P. Wihler,
In this article we propose a class of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical solution of a second-order quasilinear elliptic boundary value problem of monotone type. The key idea in this setting is to first discretise the underlying nonlinear problem on a coarse finite element space $V({{\mathcal {T}_{H}}},\boldsymbol {P})$ . The resulting 'coarse' numerical solution is then exploited to provide the necessary data needed to linearise the underlying ...
Tópico(s): Electromagnetic Simulation and Numerical Methods
2012 - Springer Science+Business Media | Journal of Scientific Computing
... Scholar[15] E. Tadmor, Finite-difference, spectral and Galerkin methods for time-dependent problems, ICASE Report, 83- ... No. 1 | 1 Jul 2007 Cross Ref Adaptive Galerkin boundary element methods with panel clusteringNumerische Mathematik, Vol. ... Stability Analysis of Finite Difference, Pseudospectral and Fourier–Galerkin Approximations for Time-Dependent ProblemsEitan TadmorSIAM Review, Vol. ...
Tópico(s): Mathematical functions and polynomials
1986 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis