@Article{AAMM-1-201, author = {Vejchodský , Tomáš and Šolín , Pavel}, title = {Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by $hp$-FEM}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {2}, pages = {201--214}, abstract = {

We present a proof of the discrete maximum principle (DMP) for the 1D Poisson equation $−u''=f$ equipped with mixed Dirichlet-Neumann boundary conditions. The problem is discretized using finite elements of arbitrary lengths and polynomial degrees ($hp$-FEM). We show that the DMP holds on all meshes with no limitations to the sizes and polynomial degrees of the elements.

}, issn = {2075-1354}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aamm/10174.html} }