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- Nathan V. Roberts, Tan Bui-Thanh, Leszek F. Demkowicz
- Computers & Mathematics with Applications
- 2014

We discuss well-posedness and convergence theory for the DPG method applied to a general system of linear Partial Differential Equations (PDEs) and specialize the results to the classical Stokes problem. The Stokes problem is an iconic troublemaker for standard Bubnov Galerkin methods; if discretizations are not carefully designed, they may exhibit… (More)

- Nathan V. Roberts
- Computers & Mathematics with Applications
- 2014

- Nathan V. Roberts, Leszek F. Demkowicz, Robert Moser
- J. Comput. Physics
- 2015

- Nathan Vanderkooy Roberts, Todd Arbogast, +4 authors Robert Moser
- 2013

- Keith, P. Knechtges, +4 authors B. Keitha

We explore a vexing benchmark problem for viscoelastic fluid flows with the discontinuous Petrov-Galerkin (DPG) finite element method of Demkowicz and Gopalakrishnan [1, 2]. In our analysis, we develop an intrinsic a posteriori error indicator which we use for adaptive mesh generation. The DPG method is useful for the problem we consider because the method… (More)

- Eunjee Song, Nathan V. Roberts
- SSIRI
- 2008

Aspect-oriented modeling (AOM) techniques have received increasing attention as solution to separating crosscutting concerns, such as logging, access control, from other application design concerns. In AOM, crosscutting concerns are modeled as aspect models and other application features are modeled as a primary model. Composing aspect models with a primary… (More)

- Nathan V. Roberts, Jesse Chan
- ArXiv
- 2016

The discontinuous Petrov-Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan [15, 17] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. A key question that has not yet been answered in general—though there are some results for Poisson, e.g.—is how best to precondition the DPG… (More)

- Nathan V. Roberts, Eunjee Song, Paul C. Grabow
- SAC
- 2009

A key problem in software development is producing systems that are maintainable even as the concerns at play evolve. Aspect-oriented programming (AOP) seeks to foster maintainability by isolating the specifications of cross-cutting concerns, allowing them to be modified in relative isolation from the rest of the system. Research in aspect-oriented modeling… (More)

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