A Dual Least-Squares Finite Element Method for Linear Hyperbolic PDEs: A Numerical Study

Luke Olson

Department of Applied Mathematics, 526 UCB
University of Colorado at Boulder
Boulder, CO 80309-0526

Tom Manteuffel, Steve McCormick, Hans De Sterck


Abstract

We develop a least-squares finite element method for linear Partial Differential Equations (PDEs) of hyperbolic type. This formulation allows for discontinuities in the numerical approximation and yields a linear system which can be handled efficiently by Algebraic Multigrid solvers.

We pose the classical advection equation as a ``dual''-type problem and relate the formulation to previous attempts. Convergence properties and solution quality for discontinuous solutions are investigated for standard, conforming finite element spaces on quasi-uniform tessellations of the domain and for the general case when the flow field is not aligned with the computational mesh. Algebraic Multigrid results are presented for the linear system arising from the discretization and we study the success of this solver.

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