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We consider isogeometric discretizations of the Poisson model problem, focusing on high polynomial degrees and strong hierarchical refinements. We derive a posteriori error estimates by equilibrated fluxes, i.e., vector-valued mapped…

Numerical Analysis · Mathematics 2024-03-01 Gregor Gantner , Martin Vohralík

This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…

Numerical Analysis · Mathematics 2020-11-30 Lukas Kogler , Joachim Schöberl

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

We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The…

Numerical Analysis · Mathematics 2019-04-16 Zhaowei Liu , Musabbir Majeed , Fehmi Cirak , Robert N. Simpson

We study a recent formulation for fluid-structure interaction problems based on the use of a distributed Lagrange multiplier in the spirit of the fictitious domain approach. In this paper, we focus our attention on a crucial computational…

Numerical Analysis · Mathematics 2022-10-26 Daniele Boffi , Fabio Credali , Lucia Gastaldi

This paper is concerned with the construction of graded meshes for approximating so-called singular solutions of elliptic boundary value problems by means of multipatch discontinuous Galerkin Isogeometric Analysis schemes. Such solutions…

Numerical Analysis · Mathematics 2015-12-03 Ulrich Langer , Angelos Mantzaflaris , Stephen E. Moore , Ioannis Toulopoulos

We discuss vertex patch smoothers as overlapping domain decomposition methods for fourth order elliptic partial differential equations. We show that they are numerically very efficient and yield high convergence rates. Furthermore, we…

Numerical Analysis · Mathematics 2025-06-23 Julius Witte , Cu Cui , Francesca Bonizzoni , Guido Kanschat

We design and analyze an iterative two-grid algorithm for the finite element discretizations of strongly nonlinear elliptic boundary value problems in this paper. We propose an iterative two-grid algorithm, in which a nonlinear problem is…

Numerical Analysis · Mathematics 2023-05-04 Jiajun Zhan , Lei Yang , Xiaoqing Xing , Liuqiang Zhong

In this paper we propose a new class of preconditioners for the isogeometric discretization of the Stokes system. Their application involves the solution of a Sylvester-like equation, which can be done efficiently thanks to the Fast…

Numerical Analysis · Mathematics 2018-05-23 Monica Montardini , Giancarlo Sangalli , Mattia Tani

In this paper, we propose an extended mixed finite element method for elliptic interface problems. By adding some stabilization terms, we present a mixed approximation form based on Brezzi-Douglas-Marini element space and the piecewise…

Numerical Analysis · Mathematics 2022-03-14 Pei Cao , Jinru Chen , Feng Wang

Locking is a common effect in finite element and isogeometric analysis. In the case of plates, transverse shear locking is most prominent, for shells several other types of locking exist. A common cure are mixed methods that introduce…

Numerical Analysis · Mathematics 2026-02-26 Lisa Stammen , Wolfgang Dornisch

We consider dual-primal isogeometric tearing and interconnection (IETI-DP) solvers for multi-patch geometries in Isogeometric Analysis. Recently, the authors have published a convergence analysis for those solvers that is explicit in both…

Numerical Analysis · Mathematics 2021-03-09 Rainer Schneckenleitner , Stefan Takacs

In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph…

Algebraic Topology · Mathematics 2012-10-26 Paweł Dłotko , Hubert Wagner

In this paper, we use isogeometric Kirchhoff plates to approximate composite laminates adopting the classical laminate plate theory. Both isogeometric Galerkin and collocation formulations are considered. Within this framework, interlaminar…

Numerical Analysis · Mathematics 2020-07-21 Alessia Patton , Pablo Antolin , John-Eric Dufour , Josef Kiendl , Alessandro Reali

We present a new high order finite element method for the discretization of partial differential equations on stationary smooth surfaces which are implicitly described as the zero level of a level set function. The discretization is based…

Numerical Analysis · Mathematics 2017-04-17 Jörg Grande , Christoph Lehrenfeld , Arnold Reusken

In this paper, we consider $C^1$ cubic Powell-Sabin splines for the numerical solution of boundary value problems on planar and spatial surface domains. We first review the construction and basic properties of polynomial and rational $C^1$…

Numerical Analysis · Mathematics 2026-03-24 Jan Grošelj , Ada Šadl Praprotnik , Hendrik Speleers

This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective…

Numerical Analysis · Mathematics 2018-04-20 Riccardo Sacco , Aurelio Giancarlo Mauri , Giovanna Guidoboni

We propose a numerical method for the solution of electromagnetic problems on axisymmetric domains, based on a combination of a spectral Fourier approximation in the azimuthal direction with an IsoGeometric Analysis (IGA) approach in the…

Numerical Analysis · Mathematics 2020-07-15 Abele Simona , Luca Bonaventura , Carlo de Falco , Sebastian Schöps

The construction of volumetric parametrizations for computational domains is a key step in the pipeline of isogeometric analysis. Here, we investigate a solution to this problem based on the mesh deformation approach. The desired domain is…

Numerical Analysis · Mathematics 2019-03-25 Alexander Shamanskiy , Michael Helmut Gfrerer , Jochen Hinz , Bernd Simeon

We propose a hybridized domain decomposition formulation of the discrete fracture network model, allowing for independent discretization of the individual fractures. A natural norm stabilization, obtained by penalizing the residual measured…

Numerical Analysis · Mathematics 2024-07-29 Stefano Berrone , Silvia Bertoluzza , Stefano Scialò