Error indicators and adaptive remeshing in large deformation finite element analysis
Finite Elements in Analysis and Design
Multi-node higher order expansions of a function
Journal of Approximation Theory
Multivariate approximation by a combination of modified Taylor polynomials
Journal of Computational and Applied Mathematics
Review: A survey of the extended finite element
Computers and Structures
A mesh adaptivity procedure for CFD and fluid-structure interactions
Computers and Structures
Coupling and enrichment schemes for finite element and finite sphere discretizations
Computers and Structures
Measuring the convergence behavior of shell analysis schemes
Computers and Structures
Improved stresses for the 4-node tetrahedral element
Computers and Structures
A finite element method enriched for wave propagation problems
Computers and Structures
A stress improvement procedure
Computers and Structures
An explicit time integration scheme for the analysis of wave propagations
Computers and Structures
Towards a procedure to automatically improve finite element solutions by interpolation covers
Computers and Structures
The MITC3 shell finite element enriched by interpolation covers
Computers and Structures
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In this paper, we focus on an enriched finite element solution procedure for low-order elements based on the use of interpolation cover functions. We consider the 3-node triangular and 4-node tetrahedral displacement-based elements for two- and three-dimensional analyses, respectively. The standard finite element shape functions are used with interpolation cover functions over patches of elements to increase the convergence of the finite element scheme. The cover functions not only capture higher gradients of a field variable but also smooth out inter-element stress jumps. Since the order of the interpolations in the covers can vary, the method provides flexibility to use different covers for different patches and increases the solution accuracy without any local mesh refinement. As pointed out, the procedure can be derived from various general theoretical approaches and the basic theory has been presented earlier. We evaluate the effectiveness of the method, and illustrate the power of the scheme through the solution of various problems. The method also has potential for the development of error measures.