Work

Space-Time Reduced Element for Adaptive Finite Element Analysis of Forced Vibration of Elastic String in Maximum Norm

Year: 2026

Type: article

Abstract: This paper presents, by taking the elastic string vibration problem as the model problem, the space–time reduced element and the corresponding adaptive analysis algorithm. The solution of the space–time reduced element is extracted from the standard two-dimensional (spatial and temporal dimensions) polynomial element of the Galerkin-type by omitting the highest-degree terms, which serve as a built-in pointwise error estimator for the reduced solution. Taking the reduced solution as the final solution, the proposed adaptivity algorithm can produce solutions from the reduced element that satisfy the user-preset error tolerances in the maximum norm. Theoretical analysis and formulation are presented. Representative numerical examples, including forced vibrations with damping on an elastic foundation and moving load problems, validate the feasibility, effectiveness, and reliability of the proposed method.

Source: Applied Sciences

DOI: 10.3390/app16031632

Authors: Quan Yuan, Si Yuan

Institution: Tsinghua University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: National Natural Science Foundation of China