  Since the 1960's the finite element method emerged as a powerful tool for the
numerical simulation of countless physical phenomena or processes in applied
sciences. One of the reasons for this undeniable success is the great
versatility of the finite-element approach to deal with different types of
geometries. This is particularly true of problems posed in curved domains of
arbitrary shape. In the case of function-value Dirichlet conditions prescribed
on curvilinear boundaries method's isoparametric version for meshes consisting
of curved triangles or tetrahedra has been mostly employed to recover the
optimal approximation properties known to hold for standard straight-edged
elements in the case of polygonal or polyhedral domains. However, besides
obvious algebraic and geometric inconveniences, the isoparametric technique is
helplessly limited in scope and simplicity, since its extension to degrees of
freedom other than function values is not straightforward if not unknown. The
purpose of this paper is to propose, study and test a simple alternative that
bypasses all the above drawbacks, without eroding qualitative approximation
properties. More specifically this technique can do without curved elements and
is based only on polynomial algebra. REMARKS : First submission (dated Jan. 3,
2017) updated on Jan. 11, 2017 with the addition of a footnote on author's
research grant. A third version with several improvements was posted on Nov. 2,
2017. The fourth version incorporated some findings during the revision of a
related paper. In the fifth version, besides minor changes, the
convection-diffusion equation became the model problem; the text was reviewed
in order to highlight the advantages of the new approach over classical
techniques, more particularly by means of additional numerical examples.
