Name	Description	First appearance
$\mathbf{A}$	Diffusion matrix	Section 3.2.1
${\mathcal{A}}_{\mathbf{p}}(\check{\mathcal{Q}},{\mathbf{T}}^0)$	Anchors in T-mesh	Section 4.2.3
$\mathbf{b}$	Drift vector	Section 3.2.1
${\widehat{B}}_{i,p}$	Univariate B-spline	Section 2.1.1
$\widehat{B}[T_{i,p}]$	(Local) univariate B-spline	Section 2.1.1
${\widehat{B}}_{\mathbf{i},\mathbf{p}}$	Multivariate B-spline	Section 2.1.1
${\widehat{B}}_{\mathbf{i},\mathbf{p}}^{\ell }$	Hierarchical B-spline	Section 4.1.1
${\widehat{B}}_{\mathbf{z},\mathbf{p}}$	T-spline blending function	Section 4.2.3
${\widehat{\mathcal{B}}}^{\ell }$	Uniformly refined multivariate B-splines	Section 4.1.1
${\widehat{\mathcal{B}}}_p(T)$	Univariate B-splines	Section 2.1.1
${\widehat{\mathcal{B}}}_{\mathbf{p}}(\mathbf{T})$	Multivariate B-splines	Section 2.1.1
c	Reaction coefficient	Section 3.2.1
$C_{\mathrm{apx}}(s)$	Approximation constant for estimator	Section 5.1.4
$C_{\mathrm{apx}}^{\mathrm{tot}}(s)$	Approximation constant for total error	Section 5.2.2
$\widehat{d}$	Dimension of parametric domain	Section 2.2.1
d	Dimension of physical domain	Section 2.4
$\mathrm{d}\mathrm{l}$	Perturbation term of meshes	Section 5.1.3
${\mathcal{D}}_{\nu }$	Conormal derivative	Section 3.2.3
$\mathbf{F}$	NURBS parametrization	Section 2.4
${\mathbf{F}}_m$	NURBS parametrization of patch	Section 3.1.2
G	Fundamental solution of PDE	Section 3.3.2
h	Volume/boundary mesh-size function	Section 5.2.1/5.3.1
$\widehat{h}$	Element size in parametric domain	Section 2.2.1
$h_Q$	Element size	Section 3.1
${\widehat{\mathcal{H}}}_{\mathbf{p}}(\widehat{\mathcal{Q}},{\mathbf{T}}^0)$	Hierarchical B-splines	Section 4.1.1
${\widehat{J}}_{p,T}$	Quasi-interpolant for univariate splines	Section 2.1.2
${\widehat{J}}_{\mathbf{p},\mathbf{T}}$	Quasi-interpolant for multivariate splines	Section 2.2.2
${\widehat{J}}_{\mathbf{p},\widehat{\mathcal{Q}}}^{\mathrm{H}}$	Quasi-interpolant for hierarchical splines	Section 4.1.4
${\widehat{J}}_{\mathbf{p},\check{\mathcal{Q}}}^{\mathrm{T}}$	Quasi-interpolant for T-splines	Section 4.2.4
$\mathcal{K}$	Double-layer operator	Section 3.3.2
$\mathrm{lev}$	Level of elements in hierarchical/T-mesh	Section 4.1.1/4.2.2
$\mathrm{mot}$	Mother B-spline of truncated hierarchical B-spline	Section 4.1.2
$\mathcal{N}(\check{Q})$	Neighbors for T-splines in index domain	Section 4.2.4
$\mathcal{N}(\widehat{Q})$	Neighbors for T-splines in parametric domain	Section 4.2.4
$\mathcal{N}(Q)$	Neighbors for volume/boundary multi-patches	Section 6.1.5/7.1
${\mathcal{N}}_{\mathcal{H}}(\widehat{Q},\mu )$	Neighbors for HB-splines	Section 4.1.3
${\mathcal{N}}_{\mathcal{T}}(\widehat{Q},\mu )$	Neighbors for THB-splines	Section 4.1.3
$\mathrm{osc}$	Oscillations	Section 5.2.2
p	Polynomial degree	Section 2.1.1
$\mathbf{p}$	Polynomial degree vector	Section 2.2.1
${\mathbf{p}}_{\mathbf{F}}$	Polynomial degree vector for parametrization	Section 3.1
$\mathcal{P}$	PDE operator	Section 3.2.1
${\check{\mathcal{Q}}}_0$	Initial T-mesh of index domain	Section 4.2.2
${\widehat{\mathcal{Q}}}_0$	Initial hierarchical/T-mesh in parametric domain	Section 4.1.3/4.2.5
${\mathcal{Q}}_0$	Initial mesh	Section 5.1.1
${\widehat{\mathcal{Q}}}_{\mathbf{F}}$	Mesh of parametric domain induced by knots of parametrization	Section 3.1
${\widehat{\mathcal{Q}}}^{\ell }$	Uniformly refined mesh of parametric domain	Section 4.1.1
${\mathcal{Q}}_{\mathbf{F}}$	Mesh induced by parametrization	Section 3.1
$\widehat{\mathbb{Q}}$	Admissible hierarchical/T-meshes	Section 4.1.3/4.2.5
$\mathbb{Q}$	Admissible meshes	Section 5.1.1
${\widehat{\mathbb{Q}}}_m$	Admissible meshes of volume/boundary patch in parametric domain	Section 6.1.5/7.1
${\mathbb{Q}}_m$	Admissible meshes of volume/boundary patch	Section 6.1.5/7.1
$S_{\mathrm{ext}}(\widehat{Q})$	Support extension (for B-splines and T-splines)	Section 2.2.1/4.2.4
$S_{\mathrm{ext}}(\widehat{Q},k)$	Multilevel support extension	Section 4.1.3
$S_{\mathrm{ext}}^{\ast }(\widehat{Q})$	Modified support extension	Section 4.1.4
$\mathbb{S}$	FEM/BEM ansatz space	Section 3.2.1/3.3.2
${\widehat{\mathbb{S}}}_p(T)$	Space of univariate splines	Section 2.1.1
${\widehat{\mathbb{S}}}_{\mathbf{p}}(\mathbf{T})$	Space of multivariate splines	Section 2.2.1
${\widehat{\mathbb{S}}}_{\mathbf{p}}^{\mathrm{H}}(\widehat{Q},{\mathbf{T}}^0)$	Space of hierarchical splines	Section 4.1.1
${\widehat{\mathbb{S}}}_{\mathbf{p}}^{\mathrm{T}}(\check{\mathcal{Q}},{\mathbf{T}}^0)$	Space of T-splines	Section 4.2.3
T	Knot vector	Section 2.1.1
$T_0$	Iinitial knot vector	Section 7.3.2
${\widehat{T}}_{\mathbf{i},\mathbf{p}}^{\ell }$	Truncated hierarchical B-spline	Section 4.1.2
${\mathrm{Trunc}}^{\ell +1}$	Truncation operator	Section 4.1.2
$\mathbf{T}$	Vector of knot vectors	Section 2.2.1
${\mathbf{T}}^0$	Initial vector of knot vectors	Section 4.2.2
${\mathbf{T}}_{\mathbf{F}}$	Vector of knot vectors for parametrization	Section 3.1
${\mathbf{T}}^{\ell }$	Uniformly refined vector of knot vectors	Section 4.1.1
${\widehat{\mathcal{T}}}_{\mathbf{p}}(\widehat{\mathcal{Q}},{\mathbf{T}}^0)$	Truncated hierarchical B-splines	Section 4.1.2
$\mathbb{T}$	Admissible knot vectors for univariate refinement	Section 7.3.2
u	PDE solution	Section 3.2.1
U	Galerkin FEM approximation	Section 3.2.1
$\mathcal{V}$	Vertices of mesh	Section 7.3.1
${\mathcal{V}}_{\mathbf{F}}$	Vertices of geometry	Section 3.1.3
$\mathcal{V}$	Single-layer operator	Section 3.3.2
Z	Breakpoints	Section 2.1.1
${\widehat{\gamma }}_0$	Shape-regularity constant	Section 7.3.2
$\widehat{\Gamma }$	Parametric domain for BEM	Section 3.1
$\Gamma$	Physical domain for BEM	Section 3.1
${\Gamma }_{m,m^{\prime }}$	Interface between NURBS patches	Section 3.1.2
$\eta$	Error estimator for FEM/BEM	Section 3.2.3/3.3.4
${\widehat{\lambda }}_{i,p}$	Univariate dual functional	Section 2.1.2
${\widehat{\lambda }}_{\mathbf{i},\mathbf{p}}$	Multivariate dual functional	Section 2.2.2
${\widehat{\lambda }}_{\mathbf{i},\mathbf{p}}^{\ell }$	Dual functional for hierarchical splines	Section 4.1.4
${\widehat{\lambda }}_{\mathbf{z},\mathbf{p}}$	Dual functional for T-splines	Section 4.2.4
$\mu$	Admissibility parameter for hierarchical meshes	Section 4.1.3
$\nu$	Outer normal vector	Section 3.2.3
${\pi }^q$	Volume/boundary element-patch	Section 5.2.1/5.3.1
${\Pi }^q$	Volume/boundary element-patch (elements)	Section 5.2.1/5.3.1
$\varphi$	Solution of boundary integral equation	Section 3.3.2
$\Phi$	Galerkin BEM approximation	Section 3.2.2
$\widehat{\Omega }$	Parametric domain	Section 3.1
$\Omega$	Physical domain	Section 3.1
${\check{\Omega }}_{\mathrm{act}}$	Active region for definition of T-splines	Section 4.2.3
${\check{\Omega }}_{\mathrm{ind}}$	Index domain for definition of T-splines	Section 4.2.2
${\check{\Omega }}_{\mathrm{ip}}$	Index/parametric domain for definition of T-splines	Section 4.2.2
${\widehat{\Omega }}^{\ell }$	Nested subsets of parametric domain	Section 4.1.1
${\Omega }_m$	NURBS patch	Section 3.1.2
$⪯$	Refinement relation	Section 4.1.1
$\#$	Multiplicity of a breakpoint	Section 2.1.1
${\mathrm{\nabla }}_{\Gamma }$	Surface gradient	Section 3.3.1
$[·]$	Jump	Section 3.2.3
${⟨·;·⟩}_{\mathcal{P}}$	Bilinear form induced by PDE	Section 3.2.1