Finite element discretization of semilinear acoustic wave equations with kinetic boundary conditions

Electronic Transactions on Numerical Analysis

article

Marlis Hochbruck¹  Jan Leibold¹ 

[1] Karlsruhe Institute of Technology, Institute for Applied and Numerical Mathematics

关键词: wave equation;    dynamic boundary conditions;    nonconforming space discretization;    error analysis;    a-priori error bounds;    semilinear evolution equations;    operator semigroups;    isoparametric finite elements;   

DOI  :  10.1553/etna_vol53s522

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 摘 要 】

We consider isoparametric finite element discretizations of semilinear acoustic wave equations with kinetic boundary conditions and derive a corresponding error bound as our main result. The difficulty is that such problems are stated on domains with curved boundaries and this renders the discretizations nonconforming. Our approach is to provide a unified error analysis for nonconforming space discretizations for semilinear wave equations. In particular, we introduce a general, abstract framework for nonconforming space discretizations in which we derive a-priori error bounds in terms of interpolation, data, and conformity errors. The theory applies to a large class of problems and discretizations that fit into the abstract framework. The error bound for wave equations with kinetic boundary conditions is obtained from the general theory by inserting known interpolation and geometric error bounds into the abstract error result of the unified error analysis.

【 授权许可】

Unknown