Error analysis for local discontinuous Galerkin semidiscretization of Richards' equation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10481683" target="_blank" >RIV/00216208:11320/24:10481683 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=5k3o4E3nQY" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=5k3o4E3nQY</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/imanum/drae013" target="_blank" >10.1093/imanum/drae013</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Error analysis for local discontinuous Galerkin semidiscretization of Richards' equation

Popis výsledku v původním jazyce

This paper concerns an error analysis of the space semidiscrete scheme for the Richards&apos; equation modeling flows in variably saturated porous media. This nonlinear parabolic partial differential equation can degenerate; namely, we consider the case where the time derivative term can vanish, i.e., the fast-diffusion type of degeneracy. We discretize the Richards&apos; equation by the local discontinuous Galerkin (LDG) method, which provides high order accuracy and preserves stability. Due to the nonlinearityof the problem, special techniques for numerical analysis of the scheme are required. In particular, we combine two partial error bounds using continuous mathematical induction and derive a priori error estimates with respect to the spatial discretization parameter and the Hölder coefficient of the nonlinear temporal derivative. Finally, the theoretical results are supported by numerical experiments, including cases beyond the assumptions of the theoretical results.

Název v anglickém jazyce

Error analysis for local discontinuous Galerkin semidiscretization of Richards' equation

Popis výsledku anglicky

This paper concerns an error analysis of the space semidiscrete scheme for the Richards&apos; equation modeling flows in variably saturated porous media. This nonlinear parabolic partial differential equation can degenerate; namely, we consider the case where the time derivative term can vanish, i.e., the fast-diffusion type of degeneracy. We discretize the Richards&apos; equation by the local discontinuous Galerkin (LDG) method, which provides high order accuracy and preserves stability. Due to the nonlinearityof the problem, special techniques for numerical analysis of the scheme are required. In particular, we combine two partial error bounds using continuous mathematical induction and derive a priori error estimates with respect to the spatial discretization parameter and the Hölder coefficient of the nonlinear temporal derivative. Finally, the theoretical results are supported by numerical experiments, including cases beyond the assumptions of the theoretical results.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

IMA Journal of Numerical Analysis

ISSN

0272-4979

e-ISSN

1464-3642

Svazek periodika

45

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

51

Strana od-do

580-630

Kód UT WoS článku

001219731400001

EID výsledku v databázi Scopus

2-s2.0-85217023329