A new 3D finite element for adaptive \(h\)-refinement in 1-irregular meshes. (English) Zbl 0838.76042
A new finite element, viable for use in the three-dimensional simulation of transient physical processes with sharply varying solutions, is presented. The element is intended to function in adaptive \(h\)-refinement schemes as a versatile transition between regions of different refinement levels, ensuring interelement continuity by constructing a piecewise linear solution at the element boundaries, and retaining all degrees of freedom in the solution phase. Construction of the element shape functions is described, and a numerical example is presented which illustrates the advantages of using such an element in an adaptive refinement problem.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 86A05 | Hydrology, hydrography, oceanography |
| 86A20 | Potentials, prospecting |
Keywords:
moving-front problems; reservoir engineering; groundwater flow; interelement continuity; piecewise linear solution; element shape functionsReferences:
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