Two-grid $ H^1 $-Galerkin mixed finite elements combined with $ L1 $ scheme for nonlinear time fractional parabolic equations-Reference-Cited by-同舟云学术

Two-grid $ H^1 $-Galerkin mixed finite elements combined with $ L1 $ scheme for nonlinear time fractional parabolic equations

Published:2023 Issue:12 Volume:31 Page:7207-7223
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Pan Jun¹,Tang Yuelong²

Affiliation:

1. School of Foundation Studies, Zhejiang Pharmaceutical University, Ningbo 315500, China

2. College of Science, Hunan University of Science and Engineering, Yongzhou 425199, China

Abstract

<abstract><p>In this paper, we propose a two-grid algorithm for nonlinear time fractional parabolic equations by $ H^1 $-Galerkin mixed finite element discreitzation. First, we use linear finite elements and Raviart-Thomas mixed finite elements for spatial discretization, and $ L1 $ scheme on graded mesh for temporal discretization to construct a fully discrete approximation scheme. Second, we derive the stability and error estimates of the discrete scheme. Third, we present a two-grid method to linearize the nonlinear system and discuss its stability and convergence. Finally, we confirm our theoretical results by some numerical examples.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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