2024/11/25 by Marcus J. Grote, Omar Lakkis, Grote, Marcus J. +3 · 1 citation
Engineering · Mathematics · #35A35 #35L05 #65J10 #65M22 #65M60 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #G.1.8 #G.4 #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2411.16933
openalex publication_date 2024/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive a fully computable aposteriori error estimator for a Galerkin finite element solution of the wave equation with explicit leapfrog time-stepping. Our discrete formulation accommodates both time evolving meshes and leapfrog based local time-stepping (Diaz & Grote, 2009), which overcomes the stringent stability restriction on the time-step due to local mesh refinement. Thus we account for adaptive time-stepping with mesh change in a fully explicit time integration while retaining its efficiency. The error analysis relies on elliptic reconstructors and abstract grid transfer operators, which allows for use-defined elliptic error estimators. Numerical results using the elliptic Babuška-Rheinboldt estimators illustrate the optimal rate of convergence with mesh size of the aposteriori error estimator.