Establishes ε-robust algebraic rate bounds for P1 finite elements on special meshes and for ReLU and tanh neural networks in approximating solutions to singularly perturbed boundary value problems under low Sobolev regularity.
Brezis.Functional analysis, Sobolev spaces and partial differential equations
7 Pith papers cite this work. Polarity classification is still indexing.
7
Pith papers citing it
representative citing papers
Existence, boundary asymptotics, and uniqueness results for large solutions of semilinear Finsler p-Laplacian equations under a Keller-Osserman integrability condition.
A QTT-based solver with Helmholtz-Leray penalization in Fourier space stably computes solutions and gradients for multiscale elliptic PDEs on meshes with up to 10^37 virtual degrees of freedom in 3D.
Existence of a family of discontinuous shock wavefronts is established for bistable reaction-diffusion equations with sign-changing diffusivity where the interior reaction zero lies in the negative region, together with their speeds and an application to a mixed individual-group population model.
A convergent finite element method is constructed and analyzed for an anisotropic porous medium equation with fractional pressure, with numerical tests in 2D.
A structure-preserving LDG discretization with backward Euler for conformational conversion systems that enforces positivity, proves entropy stability and convergence, and yields existence of global weak solutions.
Proves existence and uniqueness of mean-field equilibrium in a stochastic optimal investment game with price interaction through expected production capacity, for finite and infinite time horizons, plus the deterministic counterpart.
citing papers explorer
-
Neural Networks for Singular Perturbations -- Finite Regularity
Establishes ε-robust algebraic rate bounds for P1 finite elements on special meshes and for ReLU and tanh neural networks in approximating solutions to singularly perturbed boundary value problems under low Sobolev regularity.
-
Boundary Blowup Solutions for the Finsler p-Laplacian: Wellposedness and Asymptotic Behaviour
Existence, boundary asymptotics, and uniqueness results for large solutions of semilinear Finsler p-Laplacian equations under a Keller-Osserman integrability condition.
-
Stable full-field simulation of a multiscale elliptic equation by means of Quantized Tensor Trains
A QTT-based solver with Helmholtz-Leray penalization in Fourier space stably computes solutions and gradients for multiscale elliptic PDEs on meshes with up to 10^37 virtual degrees of freedom in 3D.
-
Shock wavefronts for parabolic equations with sign-changing diffusivity
Existence of a family of discontinuous shock wavefronts is established for bistable reaction-diffusion equations with sign-changing diffusivity where the interior reaction zero lies in the negative region, together with their speeds and an application to a mixed individual-group population model.
-
Finite element approximation of an anisotropic porous medium equation with fractional pressure
A convergent finite element method is constructed and analyzed for an anisotropic porous medium equation with fractional pressure, with numerical tests in 2D.
-
Structure-preserving local discontinuous Galerkin discretization of conformational conversion systems
A structure-preserving LDG discretization with backward Euler for conformational conversion systems that enforces positivity, proves entropy stability and convergence, and yields existence of global weak solutions.
-
Existence and uniqueness results for a mean-field game of optimal investment
Proves existence and uniqueness of mean-field equilibrium in a stochastic optimal investment game with price interaction through expected production capacity, for finite and infinite time horizons, plus the deterministic counterpart.