A new mixed finite element method based on the Crank-Nicolson scheme for Burgers' equation

Xiaohui Hu; Pengzhan Huang; Xinlong Feng

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Displaying similar documents to “A new mixed finite element method based on the Crank-Nicolson scheme for Burgers' equation”

Some $R^{N}$ capacities and applications - the lemma on mixed derivatives revisited

J. Korevaar (1986)

Matematički Vesnik

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Mixed precision GMRES-based iterative refinement with recycling

Oktay, Eda, Carson, Erin

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With the emergence of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes for solving linear systems $A x = b$ have recently been developed. However, in certain settings, GMRES may require too many iterations per refinement step, making it potentially more expensive than the alternative of recomputing the LU factors in a higher precision. In this work, we incorporate the idea of Krylov subspace recycling, a well-known technique for reusing information across sequential...

Approximation from sparse grids and function spaces of dominating mixed smoothness

Winfried Sickel (2006)

Banach Center Publications

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We investigate the convergence and the rate of convergence in $| | \cdot | L_{p} | |$ , 1 < p < ∞, of a bivariate interpolating (with respect to a sparse grid) trigonometric polynomial in the framework of Sobolev spaces of dominating mixed smoothness.

The diagonal mapping in mixed norm spaces

Guangbin Ren, Jihuai Shi (2004)

Studia Mathematica

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For any holomorphic function F in the unit polydisc Uⁿ of ℂⁿ, we consider its restriction to the diagonal, i.e., the function in the unit disc U of ℂ defined by F(z) = F(z,...,z), and prove that the diagonal mapping maps the mixed norm space $H^{p, q, α} (U ⁿ)$ of the polydisc onto the mixed norm space $H^{p, q, | α | + (p / q + 1) (n - 1)} (U)$ of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.

New a posteriori $L^{\infty} (L^{2})$ and $L^{2} (L^{2})$ -error estimates of mixed finite element methods for general nonlinear parabolic optimal control problems

Zuliang Lu (2016)

Applications of Mathematics

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We study new a posteriori error estimates of the mixed finite element methods for general optimal control problems governed by nonlinear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates in $L^{\infty} (J; L^{2} (Ω))$ -norm and $L^{2} (J; L^{2} (Ω))$ -norm for both the state, the co-state and the control approximation. Such estimates, which seem to be new,...

Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures

Philippe Eyssidieux, Carlos Simpson (2011)

Journal of the European Mathematical Society

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Let $X$ be a compact Kähler manifold, $x \in X$ be a base point and $ρ : π_{1} (X, x) \to G L_{N} (C)$ be the monodromy representation of a $𝒞$ -VHS. Building on Goldman–Millson’s classical work, we construct a mixed Hodge structure on the complete local ring of the representation variety at $ρ$ and a variation of mixed Hodge structures whose monodromy is the universal deformation of $ρ$ .

Noncharacteristic mixed problems for hyperbolic systems of the first order

Ewa Zadrzyńska

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CONTENTS1. Introduction....................................................................................................................................................52. Notations and preliminaries .........................................................................................................................11 2.1. Function spaces and spaces of distributions............................................................................................11 2.2. Perturbations...

Carleson measures for weighted harmonic mixed norm spaces on bounded domains in $ℝ^{n}$

Ivana Savković (2022)

Czechoslovak Mathematical Journal

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We study weighted mixed norm spaces of harmonic functions defined on smoothly bounded domains in $ℝ^{n}$ . Our principal result is a characterization of Carleson measures for these spaces. First, we obtain an equivalence of norms on these spaces. Then we give a necessary and sufficient condition for the embedding of the weighted harmonic mixed norm space into the corresponding mixed norm space.

The graded differential geometry of mixed symmetry tensors

Andrew James Bruce, Eduardo Ibarguengoytia (2019)

Archivum Mathematicum

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We show how the theory of $ℤ_{2}^{n}$ -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such tensor fields on both flat and curved space-times are discussed.

On the existence of exactly one solution of integral equations in the space $L^{P}$ with a mixed norm

Bogdan Rzepecki (1975)

Annales Polonici Mathematici

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An example of the equation $u_{t} = u_{x x} + f (x, t, u)$ with distinct maximum and minimum solutions of a mixed problem

W. Mlak (1963)

Annales Polonici Mathematici

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Instability of mixed finite elements for Richards' equation

Březina, Jan

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Richards' equation is a widely used model of partially saturated flow in a porous medium. In order to obtain conservative velocity field several authors proposed to use mixed or mixed-hybrid schemes to solve the equation. In this paper, we shall analyze the mixed scheme on 1D domain and we show that it violates the discrete maximum principle which leads to catastrophic oscillations in the solution.