Related papers: Residual Based Error Estimator for Chemical-Mechan…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…
The present paper extends the theory of Adaptive Virtual Element Methods (AVEMs) to the three-dimensional meshes showing the possibility to bound the stabilization term by the residual-type error estimator. This new bound enables a…
We present a scalable, parallel implementation of a solver for the solution of a phase-field model for quasi-static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show…
Accurate terminal-voltage prediction underpins model-based battery management, yet low-order equivalent-circuit models (\ecm{}) lack expressiveness under transient conditions, whereas purely data-driven predictors sacrifice interpretability…
This research rigorously investigates the convergence of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in elastic solids. We specifically examine a novel Ambrosio-Tortorelli (AT1)…
An important objective of designing lithium-ion rechargeable battery cells is to maximize their rate performance without compromising the energy density, which is mainly achieved through computationally expensive numerical simulations at…
This paper develops and discusses a residual-based a posteriori error estimator for parabolic surface partial differential equations on closed stationary surfaces. The full discretization uses the surface finite element method in space and…
This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to…
Selective laser melting is receiving increasing interest as an additive manufacturing technique. Residual stresses induced by the large temperature gradients and inhomogeneous cooling process can favour the generation of cracks. In this…
Efficient computational methods that are capable of supporting experimental measures obtained at constant values of pH and redox potential are important tools as they serve to, among other things, provide additional atomic level information…
Electrochemical models offer superior interpretability and reliability for battery degradation diagnosis. However, the high computational cost of iterative parameter identification severely hinders the practical implementation of…
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessary to introduce a truncation boundary, whereby only a…
We present an energy-preserving mechanic formulation for dynamic quasi-brittle fracture in an Eulerian-Lagrangian formulation, where a second-order phase-field equation controls the damage evolution. The numerical formulation adapts in…
We develop and analyse residual-based a posteriori error estimates for the virtual element discretisation of a nonlinear stress-assisted diffusion problem in two and three dimensions. The model problem involves a two-way coupling between…
We define a generalized finite element method for the discretization of elliptic partial differential equations in heterogeneous media. An adaptive local finite element basis (AL basis) on a coarse mesh which does not resolve the matrix of…
In this paper, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H(curl) problem with inhomogeneous media and with the right-hand side only in L^2. The estimator is of the recovery…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
Cardiac muscle tissue during relaxation is commonly modelled as a hyperelastic material with strongly nonlinear and anisotropic stress response. Adapting the behavior of such a model to experimental or patient data gives rise to a parameter…
Modern computing systems are capable of exascale calculations, which are revolutionizing the development and application of high-fidelity numerical models in computational science and engineering. While these systems continue to grow in…
We study the role of numerical quadrature in residual-minimisation methods for neural network approximation of partial differential equations. We first present an abstract error framework that separates approximation, quadrature and…