Finite element mesh refinement algorithm using element residuals
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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.
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