#finite element methods try — diffusion models for protein design efficient attention beyond transformers papers like retrieval-augmented generation
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8 papers match
cs.CE 2026 ☆
Data-free neural PDE solvers based on Graph Neural Networks and weak forms Mikel M. Iparraguirre, Iciar Alfaro, David Gonzalez +1
The paper introduces a neural network that solves partial differential equations without any training data by using a graph neural network and the weak form of the equations, compu…
#graph neural networks #physics-informed neural networks #partial differential equations #weak formulation
math.NA 2026 ☆
R3MG-C: a high-order algebraic-geometric multilevel preconditioner for continuous finite element discretizations Davide Polverino, Marco Feder, Luca Heltai
The paper proposes an algebraic‑geometric multilevel preconditioner that builds a high‑order coarse space from finite element support points using an R‑tree partitioning, enabling…
#algebraic multigrid #finite element methods #preconditioning #high-order discretizations
math.NA 2026 ☆
Fully discrete least-squares splitting scheme for the Monge-Ampère equation: finite element analysis and convergence Anna Peruso
The paper introduces a fully discrete finite element framework for the two‑dimensional Dirichlet Monge‑Ampère equation using a least‑squares splitting algorithm, and provides conve…
#monge-ampere equation #finite element methods #least-squares splitting #convergence analysis
math.NA 2026 ☆
Quasi-optimal polytopal finite element methods for biharmonic equation Ngoc Tien Tran
The paper derives quasi‑optimal and lower‑order error bounds for several finite element schemes—including weak Galerkin, discontinuous Galerkin, and hybrid‑high order—applied to th…
#finite element methods #biharmonic equation #polytopal meshes #error estimation
math.NA 2026 ☆
A structure-preserving Numerical Method for the Compressible Resistive-Hall-MHD System Murtazo Nazarov, Rafael Rodriguez-Velasco, Ignacio Tomas
The paper introduces a finite element method that preserves physical properties for simulating compressible resistive Hall magnetohydrodynamics, combining explicit SSP‑RK for fluid…
#magnetohydrodynamics #hall effect #finite element methods #structure-preserving algorithms
math.NA 2026 ☆
Tensor-Network Finite Elements for Analytic Operator Equations Abhijatmedhi Chotrattanapituk, Michael J. Landry, Chu-Liang Fu +1
The paper introduces a framework that combines finite-element discretization with tensor-network representations to solve analytic operator equations, converting nonlinear PDEs int…
#finite element methods #tensor networks #operator equations #partial differential equations
math.NA 2026 ☆
Sufficient conditions for strong discrete maximum principles in finite element solutions of linear and semilinear elliptic equations Andrei Draganescu, L. Ridgway Scott
The paper presents a new technique to establish global strong discrete maximum principles for finite element solutions of linear and semilinear elliptic equations, even when standa…
#finite element methods #elliptic equations #discrete maximum principle #semilinear PDEs
math.NA 2026 ☆
Broken-space Additive Schwarz Mass Inverse Approximations and (Block) Preconditioning Oliver A. Krzysik, Ben S. Southworth, Golo A. Wimmer
The paper proposes a broken-space additive Schwarz (BRAS) method to approximate the inverse of finite-element mass matrices, showing it improves conditioning and reduces solve time…
#finite element methods #mass matrix preconditioning #additive schwarz #high-order elements
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