5 papers · 1 filter
A Fully Discrete Nonnegativity-Preserving FEM for a Stochastic Heat Equation
Owen Hearder, Claude Le Bris, Ana Djurdjevac
We consider a stochastic heat equation with nonlinear finite-rank space-coloured multiplicative noise that admits a unique nonnegative solution when given nonnegative initial data.…
A nonnegativity-preserving finite element method for a class of parabolic SPDEs with multiplicative noise
Ana Djurdjevac, Claude Le Bris, Endre Süli
We consider a prototypical parabolic SPDE with finite-dimensional multiplicative noise, which, subject to a nonnegative initial datum, has a unique nonnegative solution. Inspired b…
Certified Lumped Approximations for the Conduction Dunking Problem
Kento Kaneko, Claude Le Bris, Anthony T. Patera
We consider the dunking problem: a solid body at uniform temperature is placed in a environment characterized by farfield temperature and time-independent s…
Error Estimators for the Small-Biot Lumped Approximation for the Conduction Dunking Problem
Kento Kaneko, Claude Le Bris, Anthony T. Patera
We consider the dunking problem: a solid body at uniform temperature is placed in a environment characterized by farfield temperature and spatially uniform…
MsFEM for advection-dominated problems in heterogeneous media: Stabilization via nonconforming variants
Rutger A. Biezemans, Claude Le Bris, Frédéric Legoll +1
We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite E…