Accelerating the pace of engineering and science

# pdejmps

## Syntax

errf = pdejmps(p,t,c,a,f,u,alfa,beta,m)

## Description

errf = pdejmps(p,t,c,a,f,u,alfa,beta,m) calculates the error indication function used for adaptation. The columns of errf correspond to triangles, and the rows correspond to the different equations in the PDE system.

p andt are mesh data. For details, see initmesh.

c, a, and f are PDE coefficients. See Scalar PDE Coefficients and Coefficients for Systems of PDEs for details. c, a, and f must be expanded, so that columns correspond to triangles.

u is the solution vector. For details, see assempde.

The formula for computing the error indicator E(K) for each triangle K is

$E\left(K\right)=\alpha {‖{h}^{m}\left(f-au\right)‖}_{K}+\beta {\left(\frac{1}{2}\sum _{\tau \in \partial K}{h}_{\tau }^{2m}{\left[{n}_{\tau }\cdot \text{\hspace{0.17em}}\left(c\nabla {u}_{h}\right)\right]}^{2}\right)}^{1/2},$

where ${n}_{\tau }$ is the unit normal of edge $\tau$ and the braced term is the jump in flux across the element edge, where α and β are weight indices and m is an order parameter. The norm is an L2 norm computed over the element K. The error indicator is stored in errf as column vectors, one for each triangle in t. More information can be found in the section Adaptive Mesh Refinement.