the Finite Volume Method
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Numerical analysis of a finite volume method for a 1-D wave equation with non smooth wave speed and localized Kelvin-Voigt damping
arXiv:2502.19947v3 Announce Type: replace-cross Abstract: In this paper, we study the numerical solution of an elastic/viscoelastic wave equation with non smooth wave speed and internal localized distributed Kelvin-Voigt damping acting faraway from the boundary. Our method is based on the Finite Volume Method (FVM) and we are interested in deriving the stability estimates and the convergence of the numerical solution to the continuous one. Numerical experiments are performed to confirm the...
A high-order regularization of the non-linear shallow water equations with weakly singular shock waves and its approximation by finite volume methods
arXiv:2606.01200v1 Announce Type: cross Abstract: Considered herein is a high-order regularization of the nonlinear shallow water equations within the framework of water wave theory. The regularized system is Galilean invariant and its solutions maintain an energy level that closely matches that of the nonlinear shallow water equations.
Numerical Study of Dissipative Weak Solutions for the Euler Equations of Gas Dynamics
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A Second-order Structure-preserving Parametric FEM for Surface Evolution
arXiv:2606.08293v1 Announce Type: new Abstract: In this paper, we propose a second-order-in-time, structure-preserving, and mesh-robust parametric finite element method for surface diffusion and volume-preserving mean curvature flow. We first reformulate the original evolution equations into new systems in which the tangential motion is governed by a harmonic map heat flow. This heat flow maps a fixed reference surface onto the unknown evolving surface and drives points on the evolving...
Compact Runge-Kutta flux reconstruction methods for non-conservative hyperbolic equations
arXiv:2512.08611v2 Announce Type: replace Abstract: Compact Runge-Kutta (cRK) Flux Reconstruction (FR) methods are a variant of RKFR methods for hyperbolic conservation laws with a compact stencil including only immediate neighboring finite elements. We extend cRKFR methods to handle hyperbolic equations with stiff source terms and non-conservative products. To handle stiff source terms, we use IMplicit EXplicit (IMEX) time integration schemes such that the implicitness is local to each...
PINNOCHIO: Physics-Informed Neural Network for Coupled Hyperelastic Interface-Volume Simulation in Orthognathic Surgery
Announce Type: cross Abstract: Predicting patient-specific facial soft-tissue deformation is critical for iterative orthognathic surgery planning. However, current computational methods face a strict accuracy-efficiency trade-off: high-fidelity Finite Element Methods (FEM) are computationally prohibitive, whereas pure deep learning models often produce biomechanically inconsistent results. While Physics-Informed Neural Networks (PINNs) offer a promising avenue, learning the complex...
Optimal error estimates for a discontinuous Galerkin method on curved boundaries with polygonal meshes
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Crystal Shape and Lattice Deformation in Powder Diffraction
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