Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2607.11297

Analysis-aware interface coarsening for elliptic problems driven by an equilibrated flux estimator

Denise Grappein·Philipp Weder
View original source ↗Read source document ↗Export metadata ↓

Abstract

We propose an a posteriori error estimator that relies on an equilibrated flux reconstruction to enable analysis-aware interface coarsening decisions in elliptic interface problems. Interface coarsening consists of simplifying an internal interface that separates regions characterized by different physical properties in order to facilitate the meshing process and reduce the total number of degrees of freedom. This process extends the concept of defeaturing, where small features on the boundary of a computational domain are removed. Here, the features lie on an interior interface instead. The focus is on a Laplace problem with a discontinuous diffusion coefficient. The estimator accounts for both the modeling error arising from the interface coarsening and the numerical error from the discrete approximation of the solution to the coarsened-interface problem. It is localized on the mesh elements, and its constants explicitly track the contrast between the diffusion coefficients. The impact of different features can be assessed individually, yielding local contributions that indicate which features to coarsen and which to retain for a given mesh size. The use of an equilibrated flux reconstruction allows us to sharply bound the bulk numerical source of error. We prove the reliability of the estimator and verify it across several numerical examples, including the case where an internal interface is fully removed.

Explore related subjects

math.NAcs.NA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Denise Grappein, Philipp Weder. 2026-07-13. Analysis-aware interface coarsening for elliptic problems driven by an equilibrated flux estimator. https://arxiv.org/abs/2607.11297

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fully spectral scheme for the linear BGK equation on the whole space

In this article, we design a fully spectral method in both space and velocity for a linear inhomogeneous kinetic equation with mass, momentum and energy conservation. We focus on the linear BGK equation with a confinement potential $Φ$, even if the method could be applied to different collision operators. It is based upon the projection on Hermite polynomials in velocity and orthonormal polynomials with respect to the weight $e^{-$Φ$}$ in space. The potential $Φ$ is assumed to be a polynomial. It is, to the author's knowledge, the first scheme which preserves hypocoercive behavior in addition to the conservation laws. These different properties are illustrated numerically on both quadratic and double well potential.

math.NA↗
arXiv2026

Inverse inequalities for kernel-based approximation on bounded domains and Riemannian manifolds

This paper establishes inverse inequalities for kernel-based approximation spaces defined on bounded Lipschitz domains in $\mathbb{R}^d$ and compact Riemannian manifolds. While inverse inequalities are well-studied for polynomial spaces, their extension to kernel-based trial spaces poses significant challenges. For bounded Lipschitz domains, we extend prior Bernstein inequalities, which only apply to a limited range of Sobolev orders, to the full range of lower and upper orders, and derive Nikolskii inequalities that bound $L_\infty$ norms by $L_2$ norms. For compact Riemannian manifolds, we focus on restricted kernels, which are defined as the restriction of positive definite kernels from the ambient Euclidean space to the manifold, and prove their counterparts.

math.NA↗
arXiv2026

Error Estimates for Hyperbolic Scaling Limits of Linear Kinetic Models on Networks

This paper studies linear discrete kinetic models on networks and their asymptotic behavior in the small Knudsen number limit. For coupling conditions at an n-edge junction under a symmetric formulation, we introduce a change of variables that reformulates the system into n independent initial-boundary value problems. The asymptotic expansions are then constructed and rigorously justified by deriving an error estimate based on the energy method.

math.NA↗