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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr


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Volume 19, Issue 3

Issues

A Non-conforming Saddle Point Least Squares Approach for an Elliptic Interface Problem

Constantin Bacuta
  • Corresponding author
  • Department of Mathematics, University of Delaware, 501 Ewing Hall, Newark, Delaware 19716, USA
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/ Jacob Jacavage
Published Online: 2019-04-13 | DOI: https://doi.org/10.1515/cmam-2018-0202

Abstract

We present a non-conforming least squares method for approximating solutions of second-order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous work based on conforming discrete spaces. The SPLS method has the advantage that a discrete inf-sup condition is automatically satisfied for standard choices of test and trial spaces. We explore the SPLS method for non-conforming finite element trial spaces which allow higher-order approximation of the fluxes. For the proposed iterative solvers, inversion at each step requires bases only for the test spaces. We focus on using projection trial spaces with local projections that are easy to compute. The choice of the local projections for the trial space can be combined with classical gradient recovery techniques to lead to quasi-optimal approximations of the global flux. Numerical results for 2D and 3D domains are included to support the proposed method.

Keywords: Least Squares; Saddle Point Systems; Mixed Methods; Multilevel Methods; Uzawa Type Algorithms; Conjugate Gradient; Cascadic Algorithm; Dual DPG

MSC 2010: 74S05; 74B05; 65N22; 65N55

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About the article

Received: 2017-12-19

Revised: 2019-01-14

Accepted: 2019-03-17

Published Online: 2019-04-13

Published in Print: 2019-07-01


Funding Source: National Science Foundation

Award identifier / Grant number: DMS-1522454

The work was supported by NSF, DMS-1522454.


Citation Information: Computational Methods in Applied Mathematics, Volume 19, Issue 3, Pages 399–414, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2018-0202.

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