Continuous Galerkin finite element methods for hyperbolic\n integro-differential equations

2013/03/09 by Fardin Saedpanah, Saedpanah, Fardin · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1303.2250

openalex publication_date 2013/03/09 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

A hyperbolic integro-differential equation is considered, as a model problem,\nwhere the convolution kernel is assumed to be either smooth or no worse than\nweakly singular. Well-posedness of the problem is studied in the context of\nsemigroup of linear operators, and regularity of any order is proved for smooth\nkernels. Energy method is used to prove optimal order a priori error estimates\nfor the finite element spatial semidiscrete problem. A continuous space-time\nfinite element method of order one is formulated for the problem. Stability of\nthe discrete dual problem is proved, that is used to obtain optimal order a\npriori estimates via duality arguments. The theory is illustrated by an\nexample.\n

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