Name
Title | ||
|---|---|---|
Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part I |
Abstract | ||
|---|---|---|
First-order system least squares (FOSLS) is a recently developed methodology for solving partial differential equations. Among its advantages are that the finite element spaces are not restricted by the inf-sup condition imposed, for example, on mixed methods and that the least-squares functional itself serves as an appropriate error measure. This paper studies the FOSLS approach for scalar second-order elliptic boundary value problems with discontinuous coefficients, irregular boundaries, and mixed boundary conditions. A least-squares functional is defined, and ellipticity is established in a natural norm of an appropriately scaled least-squares bilinear form. For some geometries, this ellipticity is independent of the size of the jumps in the coefficients. The occurrence of singularities at interface corners, cross points, reentrant corners, and irregular boundary points is discussed, and a basis of singular functions with local support around singular points is established. A companion paper shows that the singular basis functions can be added at little extra cost and lead to optimal performance of standard finite element discretization and multilevel solver techniques, also independent of the size of coefficient jumps for some geometries. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1137/S0036142903427688 | SIAM J. Numerical Analysis |
Keywords | DocType | Volume |
discontinuous coefficients,singular point,finite elements,discontinuous coefficient,scalar second-order elliptic boundary,irregular boundary point,singular function,fosls formulation,companion paper,fosls approach,part ii,basis function,least-squares bilinear form,elliptic problems,first-order system,multi- level methods,consistency error term,singular basis function,discrete system,irregular boundary,mixed boundary condition,least-squares discretization,second-order elliptic problems,fosls l2 minimization problem,least square,finite element,elliptic boundary value problem,singularities,bilinear form | Journal | 43 |
Issue | ISSN | Citations |
1 | 0036-1429 | 11 |
PageRank | References | Authors |
1.24 | 5 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. Berndt | 1 | 50 | 8.27 |
| Thomas A. Manteuffel | 2 | 349 | 53.64 |
| STEPHEN F. MCCORMICK | 3 | 258 | 30.70 |
| Gerhard Starke | 4 | 125 | 27.04 |