A-posteriori error estimation for the finite point method with applications to compressible flow

• Published in: Computational mechanics Vol. 60; no. 2; pp. 219 - 233
• Main Authors: Ortega, Enrique, Flores, Roberto, Oñate, Eugenio, Idelsohn, Sergio
• Format: Journal Article Publication
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2017; Springer; Springer Nature B.V
• Subjects: Adaptivity; Approximation; Classical and Continuum Physics; Compressibilitat; Compressibility; Compressible flow; Computational fluid dynamics; Computational Science and Engineering; Differential equations; Dinàmica de fluids computacional; Engineering; Enginyeria mecànica; Error analysis; Error estimate; Finite element method; Grid refinement (mathematics); Mathematical analysis; Mecànica de fluids; Meshless; Meshless methods; Original Paper; Theoretical and Applied Mechanics; Àrees temàtiques de la UPC; Adaptivity; Compressible flow; Error estimate; Meshless
• ISSN: 0178-7675; 1432-0924; 1432-0924
• DOI: 10.1007/s00466-017-1402-7

An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.