Related papers: Residual Based Error Estimator for Chemical-Mechan…
The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…
Physico-chemical continuum battery models are typically parameterized by manual fits, relying on the individual expertise of researchers. In this article, we introduce a computer algorithm that directly utilizes the experience of battery…
The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…
An posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is…
We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates…
In this work, we investigate the numerical reconstruction of inclusions in a semilinear elliptic equation arising in the mathematical modeling of cardiac ischemia. We propose an adaptive finite element method for the resulting constrained…
The efficient and accurate simulation of material systems with defects using atomistic- to-continuum (a/c) coupling methods is a topic of considerable interest in the field of computational materials science. To achieve the desired balance…
This paper derives a posteriori error estimators for the nonlinear first-order optimality conditions associated with the electrically and flexoelectrically coupled Frank-Oseen model of liquid crystals, building on the results of [14] for…
Accurately predicting the lifespan of lithium-ion batteries is crucial for optimizing operational strategies and mitigating risks. While numerous studies have aimed at predicting battery lifespan, few have examined the interpretability of…
Despite the significant advances in deep learning over the past decade, a major challenge that limits the wide-spread adoption of deep learning has been their fragility to adversarial attacks. This sensitivity to making erroneous…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…
The sustainable utilization of lithium-ion batteries (LIBs) is crucial to the global energy transition and carbon neutrality, yet data scarcity and heterogeneity remain major barriers across remanufacturing, reusing, and recycling. This…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori…
This contribution presents a diagnosis scheme for batteries to detect and isolate internal faults in the form of small parameter changes. This scheme is based on an electrochemical reduced-order model of the battery, which allows the…
We analyze adaptive mesh-refining algorithms in the frame of boundary element methods (BEM) and the coupling of finite elements and boundary elements (FEM-BEM). Adaptivity is driven by the two-level error estimator proposed by Ernst P.…
In this paper, we study a modified residual-based a posteriori error estimator for the nonconforming linear finite element approximation to the interface problem. The reliability of the estimator is analyzed by a new and direct approach…
With the increasing number of compute components, failures in future exa-scale computer systems are expected to become more frequent. This motivates the study of novel resilience techniques. Here, we extend a recently proposed…
A new technique of residual-type a posteriori error analysis is developed for the lowest-order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension. Both centered mixed…