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Comparison of boundary and finite element methods for moving‐boundary problems governed by a potential
Author(s) -
Hume E. C.,
Brown R. A.,
Deen W. M.
Publication year - 1985
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620210710
Subject(s) - finite element method , mathematics , boundary element method , discretization , mathematical analysis , galerkin method , boundary (topology) , interpolation (computer graphics) , piecewise , boundary value problem , basis function , bounded function , laplace's equation , boundary knot method , method of fundamental solutions , laplace transform , computer science , animation , physics , computer graphics (images) , thermodynamics
Three formulations of the boundary element method (BEM) and one of the Galerkin finite element method (FEM) are compared according to accuracy and efficiency for the spatial discretization of two‐dimensional, moving‐boundary problems based on Laplace's equation. The same Euler‐predictor, trapezoid‐corrector scheme for time integration is used for all four methods. The model problems are on either a bounded or a semi‐infinite strip and are formulated so that closed‐form solutions are known. Infinite elements are used with both the BEM and FEM techniques for the unbounded domain. For problems with the bounded region, the BEM using the free‐space Green's function and piecewise quadratic interpolating functions (QBEM) is more accurate and efficient than the BEM with linear interpolation. However, the FEM with biquadratic basis functions is more efficient for a given accuracy requirement than the QBEM, except when very high accuracy is demanded. For the unbounded domain, the preferred method is the BEM based on a Green's function that satisfies the lateral symmetry conditions and which leads to discretization of the potential only along the moving surface. This last formulation is the only one that reliably satisfies the far‐field boundary condition.