2. Benchmark solution

2.1. Reference quantities and results

The analytical solution is as follows:

\(\mathrm{\nabla }\chi (X)\mathrm{=}4{r}^{2}X\). where \(\mathrm{\nabla }\chi (X)\) are the DGONFX1, DGONFX2, DGONFX3 components of field SIEF_ELGA.

\({\varepsilon }_{\mathit{xx}}(X)\mathrm{=}(\frac{{r}^{4}}{7}\mathrm{-}\frac{1}{3})+\frac{4{r}^{2}}{7}x\mathrm{\ast }x\). where \(r\) refers to the distance between the origin of the ball and the point with coordinate \(X\mathrm{=}(x,y,z)\) (component EPXX of the field EPSI_ELGA).

\({\varepsilon }_{\mathit{yy}}(X)\mathrm{=}(\frac{{r}^{4}}{7}\mathrm{-}\frac{1}{3})+\frac{4{r}^{2}}{7}y\mathrm{\ast }y\). (component EPYY of field EPSI_ELGA).

\({\varepsilon }_{\mathit{zz}}(X)\mathrm{=}(\frac{{r}^{4}}{7}\mathrm{-}\frac{1}{3})+\frac{4{r}^{2}}{7}z\mathrm{\ast }z\). (component EPZZ of field EPSI_ELGA).

\({\varepsilon }_{\mathit{xy}}(X)\mathrm{=}\frac{4{r}^{2}}{7}x\mathrm{\ast }y\). (component EPXY of field EPSI_ELGA).

\({\varepsilon }_{\mathit{xz}}(X)\mathrm{=}\frac{4{r}^{2}}{7}x\mathrm{\ast }z\). (component EPXZ of field EPSI_ELGA).

\({\varepsilon }_{\mathit{yz}}(X)\mathrm{=}\frac{4{r}^{2}}{7}y\mathrm{\ast }z\). (component EPYZ of field EPSI_ELGA).

2.2. Uncertainties about the solution

Analytical solution.