A Local Refinement Finite Element Method for Time Dependent Partial Differential Equations.
Final technical rept.,
ARMY ARMAMENT RESEARCH AND DEVELOPMENT CENTER WATERVLIET NY LARGE CALIBER WEAPON SYSTEMS LAB
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We discuss an adaptive local refinement finite element method for solving initial-boundary value problems for vector systems of partial differential equations in one space dimension and time. The method uses piecewise bilinear rectangular space-time finite elements. For each time step, grids are automatically added to regions where the local discretization error is estimated as being larger than a prescribed tolerance. We discuss several aspects of our algorithm, including the tree structure that is used to represent the finite element solution and grids, an error estimation technique, and initial and boundary conditions at coarse-fine mesh interfaces. We also present computational results for a simple linear hyperbolic problem, a problem involving Burgers equation, and a model combustion problem.
- Theoretical Mathematics