Finite Element Model
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Related Articles from SNS
A posteriori existence for the Keller-Segel model via a finite volume - finite element scheme
arXiv:2509.17710v2 Announce Type: replace Abstract: We derive two forms of conditional a posteriori error estimates for a finite volume scheme approximating the parabolic-elliptic Keller-Segel system. The estimates control the error in the $L^\infty(0,T, L^2(\Omega))$- and $L^2(0,T;H^1(\Omega))$-norm and exhibit linear convergence in the mesh size, as observed in numerical experiments. Crucially, we show that, as long as the condition of the error estimate is satisfied, a weak solution exists.
Entropy-stable and energy-conservative fully-discrete finite element method for non-isothermal phase-field models
Announce Type: new Abstract: This work presents a conforming finite-element scheme for non-isothermal phase-field systems coupled to the incompressible Navier-Stokes equations. The proposed numerical scheme preserves entropy production and total energy conservation exactly by variable transformations using entropy as main variable instead of temperature.
Finite Element-Based Material Learning via Automatic Differentiation: Learning constitutive neural network models from full-field deformation data
arXiv:2606.05199v1 Announce Type: cross Abstract: The identification of constitutive neural network models from heterogeneous full-field deformation data provides a robust alternative to traditional calibration methods based on homogeneous stress-strain experiments, particularly given the high dimensionality of trainable parameters. Existing approaches must balance generality, robustness, and computational efficiency: Conventional finite element model updating is broadly applicable but...
Finite Element-Based Material Learning via Automatic Differentiation: Learning constitutive neural network models from full-field deformation data
arXiv:2606.05199v1 Announce Type: new Abstract: The identification of constitutive neural network models from heterogeneous full-field deformation data provides a robust alternative to traditional calibration methods based on homogeneous stress-strain experiments, particularly given the high dimensionality of trainable parameters. Existing approaches must balance generality, robustness, and computational efficiency: Conventional finite element model updating is broadly applicable but...
Influence of anisotropy on the expansion performance of auxetic skin meshing geometries: a finite element study
new Abstract: This study investigates the combined effects of anisotropy and auxetic mesh geometry on the performance of skin graft expansion. Finite element models of auxetic slit-based geometries were developed and subjected to 25 percent tensile strain. Skin was modelled using an anisotropic constitutive formulation.
Multicontinuum Generalized Multiscale Finite Element Method (MC-GMsFEM). Theory and applications to upscaling of two-phase flow
arXiv:2606.01303v1 Announce Type: new Abstract: We develop a multicontinuum Generalized Multiscale Finite Element Method (MC-GMsFEM) for constructing coarse-scale models in heterogeneous media that simultaneously provide accurate numerical approximations and physically consistent macroscopic equations. Classical multiscale methods efficiently approximate fine-scale solutions on coarse grids using localized basis functions, but they do not offer a systematic pathway for deriving macroscopic...
Mesh Graph Neural Network Framework for Accelerating Finite Element Simulation for Arbitrary Geometries
arXiv:2606.08287v1 Announce Type: new Abstract: Finite element analysis (FEA) is essential for structural design but remains computationally expensive, particularly when evaluating multiple design iterations or load scenarios. Machine learning surrogate models offer a promising alternative, yet most approaches struggle with a critical limitation: generalizing across varying geometries. This work presents a mesh graph network (MGN) for predicting von Mises stress fields in 2D structural...
PDE-Agents: An LLM-Orchestrated Multi-Agent Framework for Automated Finite Element Simulations with Knowledge Graph-Augmented Reasoning
Announce Type: new Abstract: We present PDE-Agents, a multi-agent ecosystem that automates the full lifecycle of partial differential equation (PDE) / finite element method (FEM) simulations through natural-language interaction. Three specialist large language model (LLM) agents (Simulation, Analytics, Database) are orchestrated via a LangGraph supervisor, with a local open-source LLM stack (Qwen3-Coder-Next, Llama 4 Scout) on dual NVIDIA RTX PRO 6000 GPUs. The architecture is...
Well-posedness and finite element approximation of the electrostatic shear Alfv\'en wave equations
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Low-Variance Randomised Numerical Linear Algebra for Finite Element Simulation
arXiv:2606.08817v1 Announce Type: new Abstract: We present a low-variance randomised numerical linear algebra approach for multi-query finite element systems arising from parametric elliptic partial differential equations with applications to digital twins and online model calibration. The method relies on Galerkin subspace projection for reducing the dimensionality, and then combines parameter-oblivious leverage-score Bernoulli sampling with a control variates scheme to yield a...