Mesh grading in isogeometric analysis

This paper is concerned with the construction of graded meshes for approximating so-called singular solutions of elliptic boundary value problems by means of multipatch discontinuous Galerkin Isogeometric Analysis schemes. Such solutions appear, for instance, in domains with re-entrant corners on th...

Full description

Saved in:
Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2015-10, Vol.70 (7), p.1685-1700
Main Authors: Langer, Ulrich, Mantzaflaris, Angelos, Moore, Stephen E., Toulopoulos, Ioannis
Format: Article
Language:English
Subjects:
Approximation
Boundaries
Computer Science
Construction
Convergence
Corners
Discontinuous coefficients
Domains with geometric singular points or edges
Elliptic boundary value problems
Grading
Isogeometric analysis
Mathematical analysis
Mathematical models
Mathematics
Mesh grading
Modeling and Simulation
Numerical Analysis
Recovering optimal convergence rates
Symbolic Computation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper is concerned with the construction of graded meshes for approximating so-called singular solutions of elliptic boundary value problems by means of multipatch discontinuous Galerkin Isogeometric Analysis schemes. Such solutions appear, for instance, in domains with re-entrant corners on the boundary of the computational domain, in problems with changing boundary conditions, in interface problems, or in problems with singular source terms. Making use of the analytic behavior of the solution, we construct the graded meshes in the neighborhoods of such singular points following a multipatch approach. We prove that appropriately graded meshes lead to the same convergence rates as in the case of smooth solutions with approximately the same number of degrees of freedom. Representative numerical examples are studied in order to confirm the theoretical convergence rates and to demonstrate the efficiency of the mesh grading technology in Isogeometric Analysis.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2015.03.011