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- W2966452845 abstract "Abstract In the first part of this chapter, the basic algorithmic structure and performance characteristics of the p ‐version of the finite element method (FEM) are surveyed with reference to elliptic problems in solid mechanics. For this class of problems, the theoretical basis of the p ‐version is fully established, and a very substantial amount of engineering experience covering linear and nonlinear applications is available. It is shown that p ‐extensions on properly designed meshes make realization of exponential rates of convergence in practical computations possible and provide for the estimation and control of relative errors in terms of any quantity of interest. In the second part, the p ‐version of the FEM is extended to a high‐order fictitious domain approach, the finite cell method (FCM). While the FCM inherits the advantages of the p ‐version with respect to accuracy and robustness, it relieves analysts from the necessity of generating finite element meshes. Thus, it strongly supports the analysis of problems with highly complicated geometry, for which meshing with finite elements would be very difficult. Given the growing demand for verified numerical solutions, the p ‐version of the finite element and FCMs are expected to play an increasingly important role." @default.
- W2966452845 created "2019-08-13" @default.
- W2966452845 creator A5059852244 @default.
- W2966452845 creator A5071118678 @default.
- W2966452845 creator A5079420272 @default.
- W2966452845 date "2017-12-15" @default.
- W2966452845 modified "2023-10-12" @default.
- W2966452845 title "The<i><scp>p</scp></i>‐Version of the Finite Element and Finite Cell Methods" @default.
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