324 citations · 636 across the 33 of their papers we have counts for
7 papers · 1 filter
A priori error estimates of regularized elliptic problems
Luca Heltai, Wenyu Lei
Approximations of the Dirac delta distribution are commonly used to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. In this w…
The deal.II finite element library: design, features, and insights
Daniel Arndt, Wolfgang Bangerth, Denis Davydov +7
deal.II is a state-of-the-art finite element library focused on generality, dimension-independent programming, parallelism, and extensibility. Herein, we outline its primary design…
Propagating geometry information to finite element computations
Luca Heltai, Wolfgang Bangerth, Martin Kronbichler +1
The traditional workflow in continuum mechanics simulations is that a geometry description -- for example obtained using Constructive Solid Geometry or Computer Aided Design tools…
Multiscale modeling of vascularized tissues via non-matching immersed methods
Luca Heltai, Alfonso Caiazzo
We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thi…
Multiscale modeling of fiber reinforced materials via non-matching immersed methods
Giovanni Alzetta, Luca Heltai
Fiber reinforced materials (FRMs) can be modeled as bi-phasic materials, where different constitutive behaviors are associated with different phases. The numerical study of FRMs th…
Error estimates in weighted Sobolev norms for finite element immersed interface methods
Luca Heltai, Nella Rotundo
When solving elliptic partial differential equations in a region containing immersed interfaces (possibly evolving in time), it is often desirable to approximate the problem using…
Quasi-optimal mesh sequence construction through Smoothed Adaptive Finite Element Method
Ornela Mulita, Stefano Giani, Luca Heltai
We propose a new algorithm for Adaptive Finite Element Methods (AFEMs) based on smoothing iterations (S-AFEM), for linear, second-order, elliptic partial differential equations (PD…