Abstract
The coupling techniques of simplified hybrid plus penalty functions are first presented for matching the Ritz-Galerkin method and thek(k>-1)-order Lagrange finite element methods to solve complicated problems of elliptic equations, homogeneous or nonhomogeneous, in particular with singularities or unbounded domains. Optimal convergence rates of numerical solutions have been proved in the Sobolev norms. Moreover, the theoretical results obtained in this paper have been verified by numerical experiments for the singular Motz problem.
Zusammenfassung
Es werden Koppelungstechniken zwischen der Ritz-Galerkin- und der Lagrange-Finite-Elemente-Methode der Ordnungk≥1 vorgestellt, die aus einer Kombination von hybriden Techniken und Straffunktionstechniken bestehen. Mit ihrer Hilfe werden komplizierte Probleme bei homogenen und inhomogenen elliptischen Gleichungen gelöst, insbesondere mit Singularitäten oder auf unbeschränkten Bereichen. Für die numerischen Lösungen werden optimale Konvergenzraten in Sobolev-Normen bewiesen. Diese theoretischen Ergebnisse werden in numerischen Experimenten für die singuläre Motz-Gleichung verifiziert.
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Li, Z.C., Bui, T.D. A new kind of combinations between the Ritz-Galerkin and finite element methods for singularity problems. Computing 40, 29–50 (1988). https://doi.org/10.1007/BF02242188
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DOI: https://doi.org/10.1007/BF02242188