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Béatrice Rivière
Researcher at Rice University
Publications - 153
Citations - 6150
Béatrice Rivière is an academic researcher from Rice University. The author has contributed to research in topics: Discontinuous Galerkin method & Finite element method. The author has an hindex of 35, co-authored 145 publications receiving 5385 citations. Previous affiliations of Béatrice Rivière include University of Pittsburgh & University of Texas at Austin.
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Discontinuous Galerkin methods for solving elliptic and parabolic equations : theory and implementation
TL;DR: Discontinuous Galerkin methods for solving partial differential equations, developed in the late 1990s, have become popular among computational scientists and engineers who work in fluid dynamics and solid mechanics and want to use DG methods for their numerical results.
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Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I
TL;DR: In this paper, three Galerkin methods using discontinuous approximation spaces are introduced to solve elliptic problems and the underlying bilinear form for all three methods is the same and is nonsymmetric.
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A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems
TL;DR: This work analyzes three discontinuous Galerkin approximations for solving elliptic problems in two or three dimensions and proves hp error estimates in the H1 norm, optimal with respect to h, the mesh size, and nearly optimal withrespect to p, the degree of polynomial approximation.
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Multiphysics simulations: Challenges and opportunities
David E. Keyes,Lois Curfman McInnes,Carol S. Woodward,William Gropp,Eric Myra,Michael Pernice,John B. Bell,Jed Brown,Alain Clo,Jeffrey M. Connors,Emil M. Constantinescu,Donald Estep,Katherine J. Evans,Charbel Farhat,Ammar Hakim,Glenn E. Hammond,Glen A. Hansen,Judith Hill,Tobin Isaac,Xiangmin Jiao,Kirk E. Jordan,Dinesh K. Kaushik,Efthimios Kaxiras,Alice Koniges,Kihwan Lee,P. Aaron Lott,Qiming Lu,John H. Magerlein,Reed M. Maxwell,Michael McCourt,Miriam Mehl,Roger P. Pawlowski,Amanda Randles,Daniel R. Reynolds,Béatrice Rivière,Ulrich Rüde,Timothy D. Scheibe,John N. Shadid,Brendan Sheehan,Mark S. Shephard,Andrew R. Siegel,Barry Smith,Xian-Zhu Tang,Cian R. Wilson,Barbara Wohlmuth +44 more
TL;DR: This study considers multiphysics applications from algorithmic and architectural perspectives, where “algorithmic” includes both mathematical analysis and computational complexity, and “architectural’ includes both software and hardware environments.
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Locally Conservative Coupling of Stokes and Darcy Flows
Béatrice Rivière,Ivan Yotov +1 more
TL;DR: A locally conservative numerical method for solving the coupled Stokes and Darcy flows problem is formulated and analyzed and a discrete inf-sup condition and optimal error estimates are derived.