diff --git a/src/materials/element_wise_scalar_diffusion.jl b/src/materials/element_wise_scalar_diffusion.jl
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+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+    ElementWiseScalarDiffusion <: AbstractMaterial
+
+Piecewise **constant** isotropic scalar conductivity on each volume element
+(index matches `mesh.connectivity` order): at quadrature points of element `e`
+the tensor is `λ_by_elem[e] · I`.
+
+Used with [`HeatKernel`](@ref) and either [`Temperature`](@ref) (thermal
+conductivity values in ``k``) or [`PressurePotential`](@ref) (hydraulic
+conductivity ``K``). For a spatially smooth ``λ(x)``, refine the mesh or use
+per-region assembly; truly pointwise ``λ`` at quadrature nodes is not covered
+here.
+
+# Example
+
+```julia
+# Two bricks along x with different K; λ_by_elem[i] is conductivity of element i.
+mat = ElementWiseScalarDiffusion([1.0, 4.0])
+kernel = HeatKernel(ContinuumFormulation{FullThreeD}(), mat, PressurePotential())
+```
+"""
+
+struct ElementWiseScalarDiffusion <: AbstractMaterial
+    λ_by_elem::Vector{Float64}
+end
+
+material_behavior(::ElementWiseScalarDiffusion) = StatelessConstantTangent()
+supported_physics(::ElementWiseScalarDiffusion) = (Thermal{3}(),)
+required_state_variables(::ElementWiseScalarDiffusion) = ()