Finite element mesh refinement algorithm using element residuals
An algorithm is formulated for automatic adaptive refinement of finite element meshes for 2-point boundary-value problems. Global a posteriori error bounds by the residual lead to the use of element residuals as a relative measure of solution accuracy on the elements. A statistical procedure is devised to establish the regions of refinement and the degree of refinement necessary. An associated research code has been applied to linear and nonlinear problems including applications of boundary-layer type. Numerical experiments demonstrate the effectiveness of the scheme and its value in efficient solution of nonlinear problems.
Unable to display preview. Download preview PDF.
- 1.Pearson, C.E., "A Numerical Method for Ordinary Differential Equations of Boundary Layer Type," J. Math. Phys., Vol. 47, pp. 134–154, 1968.Google Scholar
- 2.Humphrey, D., and Carey, G.F., "Adaptive Mesh Refinement Algorithm Using Element Residuals," TICOM Report 78-1, Texas Institute for Computational Mechanics, January, 1978.Google Scholar
- 3.Carey, G.F., and Humphrey, D., "Adaptive Refinement Using Residuals," (in preparation).Google Scholar
- 4.Oden, J.T., and Reddy, J.N., Mathematical Foundations of the Finite Element Method, Wiley Interscience, 1976.Google Scholar
- 5.Carey, G.F., and Finlayson, B.A., "Orthogonal Collocation on Finite Elements," Chemical Engineering Science, Vol. 30, pp. 587–596, 1975.Google Scholar