English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We develop error estimates for the semidiscrete conservative spectral method for the approximation of the elastic and inelastic space homogeneous Boltzmann equation introduced by Gamba and Tharkabhushanam in [J. Comput. Phys., 228 (2009), pp. 2012--2036]. In addition we study the long time convergence of such semidiscrete solution to the equilibrium Maxwellian distribution that conserves the mass, momentum, and energy associated with the initial data. The numerical method is based on the Fourier transform of the collisional operator and a Lagrangian optimization correction that enforces the collision invariants, namely, conservation of mass, momentum, and energy in the elastic case, and just mass and momentum in the inelastic one. We present a detailed semidiscrete analysis on convergence of the proposed numerical method which includes the $L^{1}-L^{2}$ theory for the scheme. This analysis allows us to present, additionally, convergence in Sobolev spaces and convergence to equilibrium for the numerical ap...

Convergence and Error Estimates for the Lagrangian-Based Conservative Spectral Method for Boltzmann Equations