Finite-element methods for Maxwell's equations with stationary magnetic fields and Galerkin-wavelets methods for two-point boundary-value problems
This thesis consists of two parts. In the first, the author studies numerical methods for solving a class of partial different equations of the Sobolev type. For the semidiscretization scheme (namely, only the spatial variables are approximated by finite element method) he proves its stability and its a priori error estimates in H{sup 1}, L{sup 2} and L{sup {infinity}} norms. For piecewise linear finite element spaces, the uniform convergence is proved by a superapproximation result. The induced system of ordinary differential equations can be solved in detail. Numerical experiments are presented. In the second part, a new class of methods, the Galerkin-wavelets methods, is studied. First introduced are the wavelets with compact supports. Then the trial function space of the Galerkin method is constructed by anti-derivatives of wavelets. He derives approximation properties of these spaces and the error estimates of the Galerkin-wavelets methods in H{sup 1} and L{sup 2} norms. The methods are applied to solve two-point boundary value problems. The conjugate gradient method is proved to be very efficient for solving the induced linear system; a preconditioner is also constructed. By changing bases, the full matrices are reduced to sparse ones. Numerical experiments are also presented.
- Research Organization:
- Pennsylvania State Univ., University Park, PA (United States)
- OSTI ID:
- 5256557
- Country of Publication:
- United States
- Language:
- English
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