An Error Analysis of Conservative Space-Time Mesh Refinement Methods for the One-Dimensional Wave Equation

2005 ◽  
Vol 43 (2) ◽  
pp. 825-859 ◽  
Author(s):  
Patrick Joly ◽  
Jerónimo Rodriguez
Keyword(s):  
Wave Equation ◽  
Error Analysis ◽  
Mesh Refinement ◽  
Space Time ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

LOCAL SPACE-TIME REFINEMENT FOR THE ONE-DIMENSIONAL WAVE EQUATION

2005 ◽  
Vol 13 (03) ◽  
pp. 547-568 ◽  
Author(s):  
LAURENCE HALPERN
Keyword(s):  
Wave Equation ◽  
Domain Decomposition ◽  
Constant Velocity ◽  
Space Time ◽  
Strong Sense ◽  
One Dimensional ◽  
Local Space ◽  
Second Order In Time ◽  
The One ◽  
Dimensional Wave

We presented recently a new method to design a non-conforming space-time scheme for the wave equation.10 We introduce here a new concept of stability for domain decomposition, including perturbations on the boundaries of the numerical subdomains. We prove that our scheme is stable in that strong sense, and overall second order in time and space, for a constant velocity.

Thermally corrected solutions of the one-dimensional wave equation for the laser-induced ultrasound

2021 ◽  
Vol 130 (2) ◽  
pp. 025104
Author(s):  
Misael Ruiz-Veloz ◽  
Geminiano Martínez-Ponce ◽  
Rafael I. Fernández-Ayala ◽  
Rigoberto Castro-Beltrán ◽  
Luis Polo-Parada ◽  
...  
Keyword(s):  
Wave Equation ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

scholarly journals Сlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

2020 ◽  
Vol 64 (6) ◽  
pp. 657-662
Author(s):  
V. I. Korzyuk ◽  
J. V. Rudzko
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Smooth Boundary ◽  
Analytical Form ◽  
Initial Condition ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.

Sign in / Sign up

Export Citation Format

Share Document