Locally-corrected spectral methods and overdetermined elliptic systems
نویسندگان
چکیده
منابع مشابه
Locally-corrected spectral methods and overdetermined elliptic systems
We present fast locally-corrected spectral methods for linear constant-coefficient elliptic systems of partial differential equations in d-dimensional periodic geometry. First, arbitrary second-order elliptic systems are converted to overdetermined first-order systems. Overdetermination preserves ellipticity, while first-order systems eliminate mixed derivatives, resolve convection-diffusion co...
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may very well vanish on a set of positive measure without vanishing identically. Here we explain these different behaviors in terms of geometric objects associated to each system, namely, the family of orbits of the system (0.1) (see Section 3 for precise definitions). Since the properties involved do not change if each vector Lj in (0.1) is replaced by a vector L′j = ∑ k ajk(x)Lk where the smo...
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We consider the following overdetermined boundary value problem: ∆u+ λu+ μ = 0 in Ω, u = 0 on ∂Ω and ∂u/∂n = c on ∂Ω, where c 6= 0, λ and μ are real constants and Ω ⊂ R is a smooth bounded convex open set. We first show that it may happen that the problem has no solution. Then we study the existence of solutions for a wide class of domains. 2010 Mathematics Subject Classification: 35J05, 35R30.
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Ω 7−→ λ1(Ω) , under the volume constraint Vol(Ω) = α (where α ∈ (0,Vol(M)) is fixed) are called extremal domains. Smooth extremal domains are characterized by the property that the eigenfunctions associated to the first eigenvalue of the Laplace-Beltrami operator have constant Neumann boundary data [2]. In other words, a smooth domain is extremal if and only if there exists a positive function ...
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2007
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2006.11.017