Analysis

The analysis module is, currently, one of the smallest module in Mantis. It provides a few functions to compute the - and -norms either globally or per element.

Mantis.Analysis.L2_norm Function

julia

L2_norm(
    u::Forms.AbstractForm{manifold_dim},
    dΩ::Quadrature.AbstractGlobalQuadratureRule{manifold_dim},
) where {manifold_dim}

Compute the -norm of the given form u using the given quadrature dΩ. See also L2_norm_per_element.

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Mantis.Analysis.Linf_norm Function

julia

Linf_norm(
    u::Forms.AbstractForm{manifold_dim}, xi::Points.AbstractPoints{manifold_dim}
) where {manifold_dim}
Linf_norm(
    u::Forms.AbstractForm{manifold_dim},
    dΩ::Quadrature.AbstractGlobalQuadratureRule{manifold_dim},
) where {manifold_dim}

Compute the -norm of the given form u by evaluating u at xi, or the nodes of dΩ. See also Linf_norm_per_element.

source

Mantis.Analysis.L2_norm_per_element Function

julia

L2_norm_per_element(
    u::Forms.AbstractForm{manifold_dim},
    dΩ::Quadrature.AbstractGlobalQuadratureRule{manifold_dim},
) where {manifold_dim}

Compute the -norm per element of the given form u using the given quadrature dΩ. See also L2_norm.

source

Mantis.Analysis.Linf_norm_per_element Function

julia

Linf_norm_per_element(
    u::Forms.AbstractForm{manifold_dim}, xi::Points.AbstractPoints{manifold_dim}
) where {manifold_dim}
Linf_norm_per_element(
    u::Forms.AbstractForm{manifold_dim},
    dΩ::Quadrature.AbstractGlobalQuadratureRule{manifold_dim},
) where {manifold_dim}

Compute the -norm per element of the given form u by evaluating u at xi, or the nodes of dΩ. See also Linf_norm.

source

Analysis ​

Analysis