Adaptivity is an active research area involving either remeshing or increased interpolation order during the solution process. The method is particularly effective in fluid FLOW, heat transfer, and structural analysis. The use of MESH refinement has been especially effective in aerodynamic simulations for accurately capturing shock locations in COMPRESSIBLE flow. Generally, there are two types of adaptation: h-adaptation (mesh refinement), where the element size varies while the orders of the shape FUNCTIONS arekept constant; p-adaptation, where the element size is constant while the orders of the shape functions are increased (linear, quadratic, cubic, etc.). Adaptive remeshing (known as r-adaptation) employs a spring analogy to redistribute the nodes in an existing mesh -no new nodes are added; the accuracy of the solution is limited by the initial number of nodes and elements. In mesh refinement (h-adaptation), individual elements are subdivided without altering their original position. The use of hp-adaptation includes both h- and p-adaptation strategies and produces exponential convergence rates. Both mesh refinement and adaptive remeshing are now routinely used in many commercial codes. A spectral element is a special class of FEM that USES a series of orthogonal basis functions whereby the unknown terms are solved at selected spectral nodes; the method is stable and highly accurate, but can become time consuming.

Adaptivity is an active research area involving either remeshing or increased interpolation order during the solution process. The method is particularly effective in fluid flow, heat transfer, and structural analysis. The use of mesh refinement has been especially effective in aerodynamic simulations for accurately capturing shock locations in compressible flow. Generally, there are two types of adaptation: h-adaptation (mesh refinement), where the element size varies while the orders of the shape functions arekept constant; p-adaptation, where the element size is constant while the orders of the shape functions are increased (linear, quadratic, cubic, etc.). Adaptive remeshing (known as r-adaptation) employs a spring analogy to redistribute the nodes in an existing mesh -no new nodes are added; the accuracy of the solution is limited by the initial number of nodes and elements. In mesh refinement (h-adaptation), individual elements are subdivided without altering their original position. The use of hp-adaptation includes both h- and p-adaptation strategies and produces exponential convergence rates. Both mesh refinement and adaptive remeshing are now routinely used in many commercial codes. A spectral element is a special class of FEM that uses a series of orthogonal basis functions whereby the unknown terms are solved at selected spectral nodes; the method is stable and highly accurate, but can become time consuming.