相关论文: Data-based Adaptive Refinement of Finite Element T…

In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…

The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence…

This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…

Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…

In computational engineering, ensuring the integrity and safety of structures in fields such as aerospace and civil engineering relies on accurate stress prediction. However, analytical methods are limited to simple test cases, and…

Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattered data interpolation in a d-dimensional space, however,…

For adaptive mixed finite element methods (AMFEM), we first introduce the data oscillation to analyze, without the restriction that the inverse of the coefficient matrix of the partial differential equations (PDEs) is a piecewise polynomial…

The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…

Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…

Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…

We present a simple, PDE-based proof of the result [M. Johnson, 2001] that the error estimates of [J. Duchon, 1978] for thin plate spline interpolation can be improved by $h^{1/2}$. We illustrate that ${\mathcal H}$-matrix techniques can…

During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A levelset description of…

An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…

We introduce adaptive particle refinement for compressible smoothed particle hydrodynamics (SPH). SPH calculations have the natural advantage that resolution follows mass, but this is not always optimal. Our implementation allows the user…

We extend the finite element interpolated neural network (FEINN) framework from partial differential equations (PDEs) with weak solutions in $H^1$ to PDEs with weak solutions in $H(\textbf{curl})$ or $H(\textbf{div})$. To this end, we…

The local refinement of PHT-splines (polynomial splines over hierarchical T-meshes) is achieved by a simple cross insertion, which may introduce superfluous control points or coefficients. By allowing split-in-half in mesh refinement,…

We consider discrete Poisson interface problems resulting from linear unfitted finite elements, also called cut finite elements (CutFEM). Three of these unfitted finite element methods known from the literature are studied. All three…

This paper introduces a novel adaptive refinement strategy for Isogeometric Analysis (IGA) using Truncated Hierarchical B-splines (THB-splines). The proposed strategy enhances locally-refined meshes for specific applications, simplifying…

Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…

Bolted joints can exhibit nonsmooth and significantly nonlinear dynamics. Finite Element Models (FEMs) of this phenomenon require fine spatial discretizations, inclusion of nonlinear contact and friction laws, as well as geometric…