***disc_error_estimation

Description

This command drives the computation of the finite element estimated solution error due to mesh discretization. All available methods are based on the errors indicators of type Zienkiewicz and Zhu (ZZ).

Syntax

The command has the following syntax:

***disc_error_estimator \(~\,\) **estimator estimator-type \(~\,\) **name error-estimation-given-name [ **elset elset-name ] [ **field field-name ] [ **quantity field-type ] [ **norm ] [ **relative_error type ] [ **metric metric-type ]

**name

is the name given to the global error estimation and also to the computed field of local contributions to the global estimation error.

**elset

denotes the element set on which the discretization error will be computed. By default, it will be computed on all elements.

**field

denotes the name of the gradient field used to estimate the error. By default the stress field is used to compute a ZZ type error estimator.

**quantity

defines the type of the gradient field used to estimate the discretization error. It can be a scalar field (SCALAR) or a tensorial field (TENSOR2). By default it takes the value TENSOR2.

norm

takes one of the values L2 or H1. It defines the norm used to estimate the error : \(L_2\) or energy norm. By default, the energy norm is used.

**relative_error

when activated, the error estimation is given as a percentage relative to either the maximum of the error contributions or the energy of the structure. The type can either be chose to be maximum or energy.

**metric

described in , it allows the computation of a mesh size map.

**estimator zz2

defines an error indicator based on the Zienkiewicz and Zhu estimator of second type for linear problems. It’s syntax is the following one :

\(~\,\) **estimator zz2 [ **quadratic ]

The quadratic option should be activated when used with quadratic finite elements.

**estimator zz2_heterogeneous

defines an error indicator based on the Zienkiewicz and Zhu estimator of second type for linear problems, but adapted to heterogeneous problems. It’s syntax is the following one:

\(~\,\) **estimator zz2_heterogeneous [ **penalization double-value ]

The indicator is implemented through a penalization technique, and may require an adjustement. When the penalization coefficient equals zero, the estimator is equivalent to the previous zz2 estimator applied on each heterogeneous element set.

**estimator zz2_incr

defines an error indicator proposed by Boroomand and Zienkiewicz for non linear problems.

**estimator mean

defines an error indicator based on the Zienkiewicz and Zhu estimator of first type for linear problems. It’s syntax is the following one:

\(~\,\) **estimator mean [ **quadratic ]

The quadratic option should be activated when used with quadratic finite elements.

Example

***disc_error_estimator
 **relative_error energy
 **field sig
 **name relative_energy_error_hole
 **elset ALL_ELEMENT
 **quantity TENSOR2
 **estimator zz2

***disc_error_estimator
 **field sig
 **name error_hole
 **elset ALL_ELEMENT
 **quantity TENSOR2
 **estimator zz2