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In this work, we consider adaptive mesh refinement for a monolithic phase-field description for fractures in brittle materials. Our approach is based on an a posteriori error estimator for the phase-field variational inequality realizing…

Numerical Analysis · Mathematics 2019-10-03 Katrin Mang , Mirjam Walloth , Thomas Wick , Winnifried Wollner

A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…

This work presents a robust and efficient sharp interface immersed boundary (IBM) framework, which is applicable for all-speed flow regimes and is capable of handling arbitrarily complex bodies (stationary or moving). The work deploys an…

Computational Physics · Physics 2021-01-22 Pradeep Kumar Seshadri , Ashoke De

We present new fault jump estimates to guide local refinement in surface approximation schemes with adaptive spline constructions. The proposed approach is based on the idea that, since discontinuities in the data should naturally…

Numerical Analysis · Mathematics 2024-06-27 Cesare Bracco , Carlotta Giannelli , Francesco Patrizi , Alessandra Sestini

We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable…

Numerical Analysis · Mathematics 2021-02-24 Sergio Rojas , David Pardo , Pouria Behnoudfar , Victor M. Calo

We propose a new practical adaptive refinement strategy for $hp$-finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-robust a posteriori error analysis, we solve two types of…

Numerical Analysis · Mathematics 2018-10-17 Patrik Daniel , Alexandre Ern , Iain Smears , Martin Vohralík

This paper presents a novel multilevel projection-based stabilization method for advection-dominated convection--diffusion problems within the framework of Isogeometric Analysis. The proposed approach extracts and penalizes fine-scale…

Numerical Analysis · Mathematics 2026-05-26 Zakaria El Hasnaoui , Ahmed Ratnani

We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…

Numerical Analysis · Mathematics 2022-02-16 Mario Amrein , Pascal Heid , Thomas P. Wihler

In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…

Numerical Analysis · Mathematics 2021-09-01 Santiago Badia , Manuel Caicedo , Alberto F. Martín , Javier Principe

A posteriori estimates give bounds on the error between the unknown solution of a partial differential equation and its numerical approximation. We present here the methodology based on H1-conforming potential and H(div)-conforming…

Numerical Analysis · Mathematics 2025-05-30 Martin Vohralík , Soleiman Yousef

Immersed boundary (IB) methods with adaptive mesh refinement (AMR) techniques are assessed for atmospheric entry applications, including effects of chemical nonequilibrium (CNE) and gas-surface interactions (GSI). The performance of a…

Fluid Dynamics · Physics 2023-09-19 Ata Onur Başkaya , Michele Capriati , Alessandro Turchi , Thierry Magin , Stefan Hickel

We propose joining a flexible mesh design with an integrated residual transcription in order to improve the accuracy of numerical solutions to optimal control problems. This approach is particularly useful when state or input trajectories…

Systems and Control · Electrical Eng. & Systems 2024-10-31 Lucian Nita , Eric C. Kerrigan

Adaptive finite element methods are a powerful tool to obtain numerical simulation results in a reasonable time. Due to complex chemical and mechanical couplings in lithium-ion batteries, numerical simulations are very helpful to…

Numerical Analysis · Mathematics 2024-04-17 Raphael Schoof , Lennart Flür , Florian Tuschner , Willy Dörfler

Adaptive mesh refinement (AMR) is a classical technique about local refinement in space where needed, thus effectively reducing computational costs for HPC-based physics simulations. Although AMR has been used for many years, little…

Fluid Dynamics · Physics 2024-05-14 Dewen Liu , Shuai He , Haoran Cheng , Yadong Zeng

A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…

Numerical Analysis · Mathematics 2016-02-16 Sara Pollock

We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2- and 3D domains, which is easy to use and avoids traversing…

Numerical Analysis · Mathematics 2022-02-08 Niklas Kolbe , Nikolaos Sfakianakis

Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…

Numerical Analysis · Mathematics 2021-12-21 Stefano Berrone , Alessandro D'Auria

We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on…

Numerical Analysis · Mathematics 2019-03-21 Alex Bespalov , Timo Betcke , Alexander Haberl , Dirk Praetorius

Adaptive meshing is a fundamental component of adaptive finite element methods. This includes refining and coarsening meshes locally. In this work, we are concerned with the red-green-blue refinement strategy in two dimensions and its…

Numerical Analysis · Mathematics 2020-10-13 Stefan A. Funken , Anja Schmidt

This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…

Numerical Analysis · Mathematics 2025-09-05 Théophile Chaumont-Frelet , Heiko Gimperlein , Ignacio Labarca-Figueroa , Jörg Nick