Publications of Douglas N. Arnold

For each of my papers you can obtain bibliographic information, or the full text (in PDF format). You can also obtain the bibliographic information for all these papers at once.

* Publication list * Papers at MathSciNet * Slides for some talks * Ph.D. theses of students I supervised

Geometric decompositions and local bases for spaces of finite element differential forms
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Finite element differential forms
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Finite elements for symmetric tensors in three dimensions
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Mixed finite element methods for linear elasticity with weakly imposed symmetry
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Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations
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Locking-free Reissner-Mindlin elements without reduced integration
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Finite element exterior calculus, homological techniques, and applications
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Differential complexes and stability of finite element methods. II. The elasticity complex
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Differential complexes and stability of finite element methods. I. The de Rham complex
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Complejos diferenciales y estabilidad numérica
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Rectangular mixed finite elements for elasticity
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A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate
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Quadrilateral H(div) finite elements
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A new first-order formulation for the Einstein equations
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Asymptotic estimates of hierarchical modeling
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Mixed finite elements for elasticity in the stress-displacement formulation
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Nonconforming mixed elements for elasticity
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Differential complexes and numerical stability
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Remarks on quadrilateral Reissner-Mindlin plate elements
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On the range of applicability of the Reissner-Mindlin and Kirchhoff-Love plate bending models
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Unified analysis of discontinuous Galerkin methods for elliptic problems
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Mixed finite elements for elasticity
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Approximation by quadrilateral finite elements
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Finite element approximation on quadrilateral meshes
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Numerical problems in general relativity
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Discontinuous Galerkin methods for elliptic problems
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Multigrid in H(div) and H(curl)
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Locally adapted tetrahedral meshes using bisection
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Tetrahedral bisection and adaptive finite elements
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Adaptive finite elements and colliding black holes
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Multigrid preconditioning in H(div) on non-convex polygons
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Dimensional reduction for plates based on mixed variational principles
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Preconditioning discrete approximations of the Reissner-Mindlin plate model (summary version for DD9 Proceedings, full version below)
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Preconditioning in H(div) and applications (summary version for DD9 Proceedings, full version below)
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Derivation and justification of plate models by variational methods
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Computer-aided instruction
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Preconditioning discrete approximations of the Reissner-Mindlin plate model
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Preconditioning in H(div) and applications
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Analysis of a linear-linear finite element for the Reissner-Mindlin plate model
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Interior estimates for a low order finite element method for the Reissner-Mindlin plate
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The partial selective reduced integration method and applications to shell problems
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Locking free finite element methods for shells
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Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model
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Local error estimates for finite element discretizations of the Stokes equations
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On nonconforming linear-constant elements for some variants of the Stokes equations
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Some new elements for the Reissner-Mindlin plate model
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Quadratic velocity/linear pressure Stokes element
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Innovative finite element methods for plates
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Mixed finite element methods for elliptic problems
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The boundary layer for the Reissner-Mindlin plate model
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Edge effects in the Reissner-Mindlin plate theory
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Coercivity of the single layer heat potential
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A uniformly accurate finite element method for the Reissner-Mindlin plate
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The delta-trigonometric method using the single-layer potential representation
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Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon
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A new mixed formulation for elasticity
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Boundary integral equations of the first kind for the heat equation
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Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials
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Continuous dependence on the elastic coefficients for a class of anisotropic materials
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The convergence of spline collocation for strongly elliptic equations on curves
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Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates
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A stable finite element for the Stokes equations
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A new mixed formulation for the numerical solution of elasticity problems
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The effect of the test functions on the convergence of spline projection
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PEERS: A new mixed finite element for plane elasticity
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A family of higher order mixed finite element methods for plane elasticity
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On the asymptotic convergence of spline collocation methods for partial differential equations
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Finite element methods: principles for their selection
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On the asymptotic convergence of collocation methods
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A spline-trigonometric Galerkin method and an exponentially convergent boundary integral method
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Selection of finite element methods
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Collocation versus Galerkin procedures for boundary integral methods
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An interior penalty finite element method with discontinuous elements
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A superconvergent finite element method for the Korteweg-deVries equation
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Discretization by finite elements of a model parameter dependent problem
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Robustness of finite element methods for a model parameter dependent problem
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Superconvergence of the finite element appoximation of the solution of a Sobolev partial differential equation in a single space variable
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Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable
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N.B. The PDF files for some of the papers were produced from scanned images of the published articles by JSTOR and are used with permission of JSTOR and the publisher.

Last modified July 10, 2007 by Douglas N. Arnold,