Portland State University. Department of Mathematics and Statistics
Term of Graduation
Date of Publication
Doctor of Philosophy (Ph.D.) in Mathematical Sciences
Mathematics and Statistics
Maxwell equations, Discretization (Mathematics), Finite element method
1 online resource (vii, 111 pages)
The aim of our work is to construct provably efficient and reliable error estimates of discretization error for Nédélec (edge) element discretizations of Maxwell's equations on tetrahedral meshes. Our general approach for estimating the discretization error is to compute an approximate error function by solving an associated problem in an auxiliary space that is chosen so that:
-Efficiency and reliability results for the computed error estimates can be established under reasonable and verifiable assumptions.
-The linear system used to compute the approximate error function has condition number bounded independently of the discretization parameter.
In many applications, it is some functional of the solution that is primarily of interest. In such cases, it makes sense to estimate and control discretization error with respect to this functional, rather than with respect to a global norm. We will also develop auxiliary subspace techniques for this kind of goal-oriented error estimation.
©2020 Ahmed El sakori
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El sakori, Ahmed, "A Posteriori Error Estimates for Maxwell's Equations Using Auxiliary Subspace Techniques" (2020). Dissertations and Theses. Paper 5599.