A reference triangular quadratic Lagrange finite element consists of a right triangle $\widehat{K}$ with unit legs $S_1$, $S_2$, a local space $\widehat{ℒ}$ of quadratic polynomials on $\widehat{K}$ and of parameters relating the values in the vertices and midpoints of sides of $\widehat{K}$ to every function from $\widehat{ℒ}$. Any isoparametric triangular quadratic Lagrange finite element is determined by an invertible isoparametric mapping ${ℱ}_h=(F_1,F_2)\in \widehat{ℒ}\times \widehat{ℒ}$. We explicitly describe such invertible isoparametric mappings ${ℱ}_h$ for which the images ${ℱ}_h\left(S_1\right)$, ${ℱ}_h\left(S_2\right)$ of the segments $S_1$, $S_2$ are segments,...

For flows with strong periodic content, time-spectral methods can be used to obtain time-accurate solutions at substantially reduced cost compared to traditional time-implicit methods which operate directly in the time domain. However, these methods are only applicable in the presence of fully periodic flows, which represents a severe restriction for many aerospace engineering problems. This paper presents an extension of the time-spectral approach...

This work aims at evaluating in practical situations the capability of the mesh refinement technique based on the multiresolution adaptive method coupled with high resolution spatial and temporal approximations, to recover elementary physical mechanisms by achieving gains in both CPU time and memory use compared to single grid computations. We first present a summary of the multiresolution procedure. We then describe MR algorithms. Finally, the evaluation of the method is presented on several well...