Convergence rates of curved boundary element methods for the 3D Laplace and Helmholtz equations

2025/07/18 by Luiz Faria, Pierre Marchand, Faria, Luiz Maltez +3
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2507.13955

openalex publication_date 2025/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish improved convergence rates for curved boundary element methods applied to the three-dimensional (3D) Laplace and Helmholtz equations with smooth geometry and data. Our analysis relies on a precise analysis of the consistency errors introduced by the perturbed bilinear and sesquilinear forms. We illustrate our results with numerical experiments in 3D based on basis functions and curved triangular elements up to order four.

Citations

• The linear sampling method for data generated by small random scatterers
• Computing singular and near-singular integrals over curved boundary elements: The strongly singular case
• The linear sampling method for random sources
• Computing weakly singular and near-singular integrals over curved boundary elements
• Planewave density interpolation methods for the EFIE on simple and\n composite surfaces
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