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Theory and practice of finite elements
I Theoretical Foundations.- 1 Finite Element Interpolation.- 2 Approximation in Banach Spaces by Galerkin Methods.- II Approximation of PDEs.- 3 Coercive Problems.- 4 Mixed Problems.- 5 First-Order… Expand
Mathematical Aspects of Discontinuous Galerkin Methods
Basic concepts.- Steady advection-reaction.- Unsteady first-order PDEs.- PDEs with diffusion.- Additional topics on pure diffusion.- Incompressible flows.- Friedhrichs' Systems.- Implementation.
Multicomponent transport algorithms
The authors present a general and self-contained theory of iterative algorithms for evaluating transport coefficients in multicomponent, and especially dilute polyatomic gas mixtures thus filling a… Expand
A Posteriori Control of Modeling Errors and Discretization Errors
We investigate the concept of dual-weighted residuals for measuring model errors in the numerical solution of nonlinear partial differential equations. The method is first derived in the case where...
A discontinuous Galerkin method with weighted averages for advection–diffusion equations with locally small and anisotropic diffusivity
We propose and analyse a symmetric weighted interior penalty method to approximate in a discontinuous Galerkin framework advection―diffusion equations with anisotropic and discontinuous diffusivity.… Expand
Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations
A continuous interior penalty hp-finite element method that penalizes the jump of the discrete solution across mesh interfaces is introduced. Error estimates are obtained for first-order and… Expand
Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier-Stokes equations
Two discrete functional analysis tools are established for spaces of piecewise polynomial functions on general meshes: (i) a discrete counterpart of the continuous Sobolev embeddings, in both… Expand
Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence
We analyze a nonlinear shock-capturing scheme for H1-conforming, piecewise-affine finite element approximations of linear elliptic problems. The meshes are assumed to satisfy two standard conditions:… Expand
An Intrinsic Criterion for the Bijectivity of Hilbert Operators Related to Friedrich' Systems
Friedrich' theory of symmetric positive systems of first-order PDE's is revisited so as to avoid invoking traces at the boundary. Two intrinsic geometric conditions are introduced to characterize… Expand
Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems
We propose and study a posteriori error estimates for convection-diffusion-reaction problems with inhomogeneous and anisotropic diffusion approximated by weighted interior-penalty discontinuous… Expand