5 papers · 1 filter
Physics-Informed Neural Network for Diffusion-Reaction Problems with Dead-Core Formation in Catalyst Slabs
Piotr Skrzypacz, Kaisar Tangirbergen, Jan Valdman
This work investigates a nonlinear two-point boundary value problem arising in diffusion--reaction processes in catalyst slabs with power-law kinetics and fractional reaction order…
Geometry-induced formation and merging of multiple dead zones in diffusion-reaction problems
Piotr Skrzypacz, Boris Golman, Jan Valdman
This study focuses on dead-core solutions for a two-dimensional isothermal reaction-diffusion problem involving a single chemical reaction described by power-law kinetics within a…
Numerical Algorithms for Partially Segregated Elliptic Systems
Farid Bozorgnia, Avetik Arakelyan, Vyacheslav Kungurtsev +1
We develop numerical methods for elliptic systems governed by a ternary partial-segregation constraint, in which three nonnegative components are required to have a vanishing point…
On Josephy-Halley method for generalized equations
Tomáš Roubal, Jan Valdman
We extend the classical third-order Halley iteration to the setting of generalized equations of the form \[ 0 \in f(x) + F(x), \] where \(f\colon X\longrightarrow Y\) is twice cont…
Verification of functional a posteriori error estimates for obstacle problem in 1D
Petr Harasim, Jan Valdman
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an ex…