Higher-order finite element methods for elliptic problems with\n interfaces

2015/05/16 by Johnny Guzmán, Guzman, Johnny, Manuel A. Sánchez +3
Computer Science · Engineering · Mathematics · #65N15 #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1505.04347

openalex publication_date 2015/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present higher-order piecewise continuous finite element methods for\nsolving a class of interface problems in two dimensions. The method is based on\ncorrection terms added to the right-hand side in the standard variational\nformulation of the problem. We prove optimal error estimates of the methods on\ngeneral quasi-uniform and shape regular meshes in maximum norms. In addition,\nwe apply the method to a Stokes interface problem, adding correction terms for\nthe velocity and the pressure, obtaining optimal convergence results.\n

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