Code to "strong norm error bounds for quasilinear wave equations under weak cfl-type conditions" (v2)

Abstract: In the present paper we consider a class of quasilinear wave equations on a smooth, bounded domain. We discretize it in space with isoparametric finite elements, and apply a semi-implicit Euler and midpoint rule as well as the exponential Euler and midpoint rule to obtain four fully discrete schemes. We derive rigorous error bounds of optimal order for the semi-discretization in space and the fully discrete methods in norms which are stronger than the classical $H^1\times L^2$ energy norm under weak CFL-type conditions. To confirm our theoretical findings, we also present numerical experiments. TechnicalRemarks: This code is used for the numerical experiment in Section 2 of the paper "Strong norm error bounds for quasilinear wave equations under weak CFL-type conditions" by Benjamin Dörich.

Part of the code relies on code written by J. Leibold in https://doi.org/10.5445/IR/1000130223 .

The computations are done in C++ using the Finite Element library deal.II; the plots then are generated with Python3.

To use this code, deal.II (release 9.5.1) has to be installed, cf. https://www.dealii.org/9.5.0

In order to compile the program, open a terminal session in this folder and call "cmake -DDEAL_II_DIR=/path/to/deal.II ." Next, call "make release" and "make". Then, one can run the commands (can be done in paralell)

./main P1 ./main P2 ./main P3 ./main P3_half

./main euler ./main midpoint

./main alpha60P1 ./main alpha60P2 ./main alpha80P1 ./main alpha80P1 ./main alpha90P1 ./main alpha90P2 ./main alpha95P1 ./main alpha95P2

to execute the code. This performs the computations and generates the files

parameters_P1.ini_space_Q1.txt parameters_P2.ini_space_Q2.txt parameters_P3.ini_space_Q3.txt parameters_P3_half.ini_space_Q3.txt

parameters_euler.ini_time_ImplEuler parameters_midpoint.ini_time_MidpointRule

parameters_alpha_60_P1.ini_space_Q1.txt parameters_alpha_60_P1.ini_space_Q2.txt

parameters_alpha_80_P1.ini_space_Q1.txt parameters_alpha_80_P2.ini_space_Q2.txt

parameters_alpha_90_P1.ini_space_Q1.txt parameters_alpha_90_P2.ini_space_Q2.txt

parameters_alpha_95_P1.ini_space_Q1.txt parameters_alpha_95_P2.ini_space_Q2.txt

in the folder "error" containing the results of the numerical experiments.

After that, the plots can be generated with the Python3 Script using in the terminal

python3 wave_non_auto_error_plots.py

in the folder "tikz".

Cite this as

Scheifinger, Malik (2023). Dataset: Code to "strong norm error bounds for quasilinear wave equations under weak cfl-type conditions" (v2). https://doi.org/10.35097/1792

DOI retrieved: 2023

Additional Info

Field Value
Imported on November 28, 2024
Last update November 28, 2024
License CC BY-NC-SA 4.0 Attribution-NonCommercial-ShareAlike
Source https://doi.org/10.35097/1792
Author Scheifinger, Malik
Given Name Malik
Family Name Scheifinger
Source Creation 2023
Publishers
Karlsruhe Institute of Technology
Production Year 2023
Publication Year 2023
Subject Areas
Name: Mathematics