Accurate error estimation is crucial in model order reduction, to obtain small reduced-order
models as well as to certify their accuracy when deployed in downstream applications such …

Nonlinear problems, which often arise in various scientific and engineering disciplines,
typically involve nonlinear equations or functions with multiple solutions. Analytical solutions …

Many time-dependent differential equations are equipped with invariants. Preserving such
invariants under discretization can be important, eg, to improve the qualitative and …

Constrained mixture models have successfully simulated many cases of growth and
remodeling in soft biological tissues. So far, extensions of these models have been …

Below the Arctic sea ice, under the right conditions, a flux of icy brine flows down into the
sea. The icy brine has a much lower fusion point and is denser than normal seawater. As a …

Numerical simulation of land models without error control can be highly inaccurate. We
present the incorporation of the Suite of Nonlinear and Differential‐Algebraic Equation …

Many complex systems can be accurately modeled as a set of coupled time-dependent
partial differential equations (PDEs). However, solving such equations can be prohibitively …

Electronic structure calculations in the time domain provide a deeper understanding of
nonequilibrium dynamics in materials. The real-time Boltzmann equation (rt-BTE), used in …

Many complex systems can be accurately modeled as a set of coupled time-dependent
partial differential equations (PDEs). However, solving such equations can be prohibitively …

Operator-splitting methods are widespread in the numerical solution of differential
equations, especially the initial-value problems in ordinary differential equations that arise …