A finite element mesh partitions the domain into simple elements, such as intervals, triangles or tetrahedra. Piecewise-polynomial trial functions and local integration assemble the stiffness matrix and mass matrix.
A family of simplicial meshes is shape-regular when the ratio of each element's diameter to its inscribed-ball radius stays uniformly bounded. This excludes degenerating shapes and makes finite element interpolation estimates uniform in the mesh size. The element sizes may still vary substantially across the domain.
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