diff --git a/src/examples.md b/src/examples.md index b8520ca9..0bf58e76 100644 --- a/src/examples.md +++ b/src/examples.md @@ -1285,6 +1285,23 @@ We recommend viewing Example 5 and Example 36 before viewing this example._

+
+##Example 41: Clamped Biharmonic + + +This example demonstrates one way that MFEM can be used to solve PDEs with higher-order derivatives by using the $C^0$ interior penalty method by [Brenner and Sung](https://doi.org/10.1007/s10915-004-4135-7). The biharmonic equation with clamped boundary conditions, + +$$\nabla^4u=1 \text{ in } \Omega,$$ +$$u=0 \text{ and } \nabla u\cdot \hat{n}=0 \text{ on } \partial\Omega,$$ + +is solved using $H^1$-conforming finite elements. Development of custom domain and face integrators are shown. See the example code for a more detailed description of the method. + +_The example has a serial ([ex41.cpp](https://github.com/mfem/mfem/blob/master/examples/ex41.cpp)) +and a parallel ([ex41p.cpp](https://github.com/mfem/mfem/blob/master/examples/ex41p.cpp)) version. +We recommend viewing Example 1 and Example 14 before viewing this example._ +
+
+
##NURBS Example 1: Poisson Problem @@ -2444,6 +2461,8 @@ function update() + showElement("ex38", all1 && all2 && all3 && none) + showElement("ex39", diffusion && h1 && galerkin && all4) + showElement("ex40", darcy && (l2 || hdiv) && (galerkin || mixed) && (gmres || newton)) + + showElement("ex41", all1 && h1 && galerkin && (pcg || amg)) + // nurbs miniapps + showElement("nurbs_ex1", diffusion && nurbs && h1) diff --git a/src/img/examples/ex41.png b/src/img/examples/ex41.png new file mode 100644 index 00000000..97d5f5b9 Binary files /dev/null and b/src/img/examples/ex41.png differ