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For functions $$u\in H^1(\Omega )$$ in a bounded polytope $$\Omega \subset {\mathbb {R}}^d$$$$d=1,2,3$$ with plane sides for $$d=2,3$$ which are Gevrey regular in $$\overline{\Omega }\backslash {\mathscr {S}}$$ with point singularities concentrated at a set $${\mathscr {S}}\subset \overline{\Omega }$$ consisting of a finite number of points in $$\overline{\Omega }$$, we prove exponential rates of convergence of hp-version continuous Galerkin finite element methods on affine families of regular, simplicial meshes in $$\Omega $$. The simplicial meshes are geometrically refined towards $${\mathscr {S}}$$ but are otherwise unstructured.

Exponential convergence in $$H^1$$ of hp-FEM for Gevrey regularity with isotropic singularities