Weighted regularization for composite materials  in electromagnetism

Patrick Ciarlet Jr.; François Lefèvre; Stéphanie Lohrengel; Serge Nicaise

Sparse finite element approximation of high-dimensional transport-dominated diffusion problems

Christoph Schwab, Endre Süli, Radu Alexandru Todor (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We develop the analysis of stabilized sparse tensor-product finite element methods for high-dimensional, non-self-adjoint and possibly degenerate second-order partial differential equations of the form $- a : \nabla \nabla u + b \cdot \nabla u + c u = f (x)$ , $x \in Ω = {(0, 1)}^{d} \subset ℝ^{d}$ , where $a \in ℝ^{d \times d}$ is a symmetric positive semidefinite matrix, using piecewise polynomials of degree ≥ 1. Our convergence analysis is based on new high-dimensional approximation results in sparse tensor-product spaces. We show that the error between the analytical solution and its stabilized sparse...

Displaying similar documents to “Weighted regularization for composite materials in electromagnetism”

Sparse finite element approximation of high-dimensional transport-dominated diffusion problems