The a posteriori error estimation in finite element method for the H (curl) problems
Abstract
This dissertation studies the a posteriori error estimation techniques for H(curl) boundary value problem originated from Maxwell's equations in three dimensions. In Chapter 1 we review the history and current status on this research topic. In Chapter 2 we review some of the fundamentals in functional analysis, prove an a priori estimate for the mixed boundary value problem, and introduce the conforming finite element methods, the Nédélec elements, for H( curl) problems. In Chapter 3 a recovery-based error estimator is introduced. In this chapter, some analytical tools are developed, including the weighted Helmholtz decompositions and weighted quasi-interpolation for H(curl) vector fields. The reliability and the efficiency bounds are established. Later in this chapter, an ad-hoc recovery-residual hybrid error estimator is introduced using a new local regularity constant idea. In Chapter 4 an equilibrated error estimator is introduced, together with some local problem solvability results. In Chapter 5 a new recovery-based error estimator is invented. By far this new recovery-based error estimator are the most efficient and reliable error estimator to date. In Chapter 6 some numerical experiments are performed to support our claims and analyses in previous chapters.
Degree
Ph.D.
Advisors
Cai, Purdue University.
Subject Area
Mathematics
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