10 papers
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.…
Effective approximations of solutions to highly oscillatory diffusion equations from coarse measurements
Claude Le Bris, Frédéric Legoll, Simon Ruget
We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only…
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…
Mathematical Modeling and Error Estimation for the Thermal Dunking Problem: A Hierarchical Approach
Theron Guo, Kento Kaneko, Claude Le Bris +1
We consider the thermal dunking problem, in which a solid body is suddenly immersed in a fluid of different temperature, and study both the temporal evolution of the solid and the…
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…