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The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
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The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.Abstract:
Preface 1. Elliptic boundary value problems 2. Introduction to the finite element method 3. Conforming finite element methods for second-order problems 4. Other finite element methods for second-order problems 5. Application of the finite element method to some nonlinear problems 6. Finite element methods for the plate problem 7. A mixed finite element method 8. Finite element methods for shells Epilogue Bibliography Glossary of symbols Index.read more
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Journal ArticleDOI
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
TL;DR: In this paper, a framework for the analysis of a large class of discontinuous Galerkin methods for second-order elliptic problems is provided, which allows for the understanding and comparison of most of the discontinuous methods that have been proposed over the past three decades.
Journal ArticleDOI
Mixed finite elements in ℝ 3
TL;DR: In this article, the authors present two families of non-conforming finite elements, built on tetrahedrons or on cubes, which are respectively conforming in the spacesH(curl) and H(div).
Book
A Posteriori Error Estimation in Finite Element Analysis
Mark Ainsworth,J. Tinsley Oden +1 more
TL;DR: In this paper, a summary account of the subject of a posteriori error estimation for finite element approximations of problems in mechanics is presented, focusing on methods for linear elliptic boundary value problems.
Journal ArticleDOI
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
Bernardo Cockburn,Chi-Wang Shu +1 more
TL;DR: It is proven that for scalar equations, the LDG methods are L2-stable in the nonlinear case and in the linear case, it is shown that if polynomials of degree k are used, the methods are kth order accurate for general triangulations.
Journal ArticleDOI
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach
TL;DR: It is shown that, using an approximate stochastic weak solution to (linear) stochastically partial differential equations, some Gaussian fields in the Matérn class can provide an explicit link, for any triangulation of , between GFs and GMRFs, formulated as a basis function representation.