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Related papers: Adaptive space-time isogeometric analysis for para…

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This paper presents a space-time finite element method (FEM) based on an unfitted mesh for solving parabolic problems on moving domains. Unlike other unfitted space-time finite element approaches that commonly employ the discontinuous…

Numerical Analysis · Mathematics 2026-04-03 Ruizhi Wang , Weibing Deng

This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner-Mindlin plates. The adaptive discretization is based on the recently developed Geometry Independent Field…

Numerical Analysis · Mathematics 2018-04-17 Peng Yu , Cosmin Anitescu , Satyendra Tomar , Stéphane Bordas , Pierre Kerfriden

This paper deals with the discrete counterpart of 2D elliptic model problems rewritten in terms of Boundary Integral Equations. The study is done within the framework of Isogeometric Analysis based on B-splines. In such a context, the…

Numerical Analysis · Mathematics 2018-02-14 A. Aimi , F. Calabrò , M. Diligenti , M. L. Sampoli , G. Sangalli , A. Sestini

We propose a new adaptive algorithm for the approximation of the Landau-Lifshitz-Gilbert equation via a higher-order tangent plane scheme. We show that the adaptive approximation satisfies an energy inequality and demonstrate numerically,…

Numerical Analysis · Mathematics 2026-02-06 Jan Bohn , Willy Dörfler , Michael Feischl , Stefan Karch

We study the numerical approximation of a coupled hyperbolic-parabolic system by a family of discontinuous Galerkin space-time finite element methods. The model is rewritten as a first-order evolutionary problem that is treated by the…

Numerical Analysis · Mathematics 2024-06-21 Markus Bause , Sebastian Franz

In isogeometric analysis, isogeometric function spaces are employed for accurately representing the solution to a partial differential equation (PDE) on a parameterized domain. They are generated from a tensor-product spline space by…

Numerical Analysis · Mathematics 2024-03-29 Dany Rios , Felix Scholz , Thomas Takacs

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…

Numerical Analysis · Mathematics 2018-08-20 Dmitriy Leykekhman , Boris Vexler

In this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. Temporal and spatial discretizations are based on Galerkin finite elements of continuous and discontinuous type. The main objectives…

Numerical Analysis · Mathematics 2024-02-06 Jan Philipp Thiele , Thomas Wick

This article investigates residual a posteriori error estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable estimates for Dirichlet and acoustic boundary conditions…

Numerical Analysis · Mathematics 2020-10-01 Heiko Gimperlein , Ceyhun Oezdemir , David Stark , Ernst P. Stephan

We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of…

Numerical Analysis · Mathematics 2021-03-24 Martin Neumuller , Iain Smears

We present a new $hp$-version space-time discontinuous Galerkin (dG) finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal/polyhedral (polytopic) elements,…

Numerical Analysis · Mathematics 2024-11-07 Andrea Cangiani , Zhaonan Dong , Emmanuil H. Georgoulis

Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time-stepping [Grote, Lakkis, Santos, 2024], we devise a space-time adaptive strategy which includes both time evolving…

Numerical Analysis · Mathematics 2026-01-07 Marcus J. Grote , Omar Lakkis , Carina S. Santos

We shall develop a fully discrete space-time adaptive method for linear parabolic problems based on new reliable and efficient a posteriori analysis for higher order dG(s) finite element discretisations. The adaptive strategy is motivated…

Numerical Analysis · Mathematics 2016-10-24 Fernando Gaspoz , Christian Kreuzer , Kunibert Siebert , Daniel Ziegler

A Skeleton-stabilized IsoGeometric Analysis (SIGA) technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed method allows utilizing identical finite dimensional spaces (with arbitrary…

We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We…

Numerical Analysis · Mathematics 2023-01-23 Santiago Badia , Hridya Dilip , Francesc Verdugo

We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…

Numerical Analysis · Mathematics 2026-04-24 Zhaonan Dong , Emmanuil H. Georgoulis , Lorenzo Mascotto , Zuodong Wang

Evolutionary deep neural networks have emerged as a rapidly growing field of research. This paper studies numerical integrators for such and other classes of nonlinear parametrizations $ u(t) = \Phi(\theta(t)) $, where the evolving…

Numerical Analysis · Mathematics 2025-01-22 Christian Lubich , Jörg Nick

This paper is concerned with using discontinuous Galerkin isogeometric analysis (dGIGA) as a numerical treatment of Diffusion problems on orientable surfaces $\Omega \subset \mathbb{R}^3$. The computational domain or surface considered…

Numerical Analysis · Mathematics 2019-04-05 Stephen Edward Moore

Multi-material problems often exhibit complex geometries along with physical responses presenting large spatial gradients or discontinuities. In these cases, providing high-quality body-fitted finite element analysis meshes and obtaining…

Numerical Analysis · Mathematics 2022-02-14 L. Noel , M. Schmidt , K. Doble , J. A. Evans , K. Maute

While the exterior Helmholtz problem with Dirichlet boundary conditions is always well-posed, the associated standard boundary integral equations are not if the squared wavenumber agrees with an eigenvalue of the interior Dirichlet problem.…

Numerical Analysis · Mathematics 2025-08-19 Théophile Chaumont-Frelet , Gregor Gantner