Error analysis for local discontinuous Galerkin semidiscretization of Richards' equation

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Error analysis for local discontinuous Galerkin semidiscretization of Richards' equation

Original language description

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.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

—

Continuities

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

Publication year

2024

Confidentiality

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

Name of the periodical

IMA Journal of Numerical Analysis

ISSN

0272-4979

e-ISSN

1464-3642

Volume of the periodical

45

Issue of the periodical within the volume

1

Country of publishing house

GB - UNITED KINGDOM

Number of pages

51

Pages from-to

580-630

UT code for WoS article

001219731400001

EID of the result in the Scopus database

2-s2.0-85217023329