Update README files for front propagation and general form PDE examples

Author: nikoscham

examples/frontPropagationScript/README.md

@@ -0,0 +1,31 @@
+<img src="https://feascript.github.io/FEAScript-website/assets/feascript-logo.png" width="80" alt="FEAScript Logo">
+
+# Front Propagation Examples
+
+This directory contains Node.js examples demonstrating how to use the FEAScript library to solve front propagation problems using the eikonal equation.
+
+## Examples
+
+#### 1. Solidification Front Propagation in a 2D Domain
+
+This example demonstrates solving an eikonal equation in a 2D domain to track the movement of a solidification interface. For detailed information on the model setup refer to the corresponding [tutorial](https://feascript.com/tutorials/solidification-front-2d.html) in the FEAScript website.
+
+## Running the Examples
+
+#### 1. Create package.json with ES module support:
+
+```bash
+echo '{"type":"module"}' > package.json
+```
+
+#### 2. Install dependencies:
+
+```bash
+npm install feascript mathjs
+```
+
+#### 3. Run the example:
+
+```bash
+node SolidificationFront2D.js
+```

examples/frontPropagationScript/solidificationFront2D/README.md

@@ -2,28 +2,4 @@
 
 ## Solidification Front Propagation in a 2D Domain
 
-This example demonstrates solving an eikonal equation in a 2D domain using the FEAScript library. The problem represents a typical solidification front propagation scenario, where the objective is to track the movement of an interface, such as in metal cooling or crystal growth processes.
-
-### Instructions
-
-This example requires the `feascript` npm package and its peer dependencies (`mathjs`). It imports FEAScript directly from the npm package and runs the simulation in a Node.js environment. To run the example, follow these instructions:
-
-1. **Create package.json with ES module support:**
-
-   ```bash
-   echo '{"type":"module"}' > package.json
-   ```
-
-2. **Install dependencies:**
-
-   ```bash
-   npm install feascript mathjs
-   ```
-
-3. **Run the example:**
-
-   ```bash
-   node SolidificationFront2D.js
-   ```
-
-**Note:** For detailed information on the model setup, boundary conditions, and simulation results, refer to the comments in the JavaScript files and the corresponding [tutorial](https://feascript.com/tutorials/SolidificationFront2D.html).
+This example demonstrates solving an eikonal equation in a 2D domain to track the movement of a solidification interface. For detailed information on the model setup refer to the corresponding [tutorial](https://feascript.com/tutorials/solidification-front-2d.html) in the FEAScript website.

examples/generalFormPDEScript/README.md

@@ -0,0 +1,31 @@
+<img src="https://feascript.github.io/FEAScript-website/assets/feascript-logo.png" width="80" alt="FEAScript Logo">
+
+# General Form PDE Examples
+
+This directory contains Node.js examples demonstrating how to use the FEAScript library to solve various partial differential equations in their general form.
+
+## Examples
+
+#### 1. Advection-Diffusion with Gaussian Source
+
+This example demonstrates solving a one-dimensional advection-diffusion problem with a Gaussian source term. The problem models the transport of a substance under the effects of both diffusion and advection. For detailed information on the model setup refer to the corresponding [tutorial](https://feascript.com/tutorials/advection-diffusion-1d.html) in the FEAScript website.
+
+## Running the Examples
+
+#### 1. Create package.json with ES module support:
+
+```bash
+echo '{"type":"module"}' > package.json
+```
+
+#### 2. Install dependencies:
+
+```bash
+npm install feascript mathjs
+```
+
+#### 3. Run the example:
+
+```bash
+node advectionDiffusion1D.js
+```

examples/generalFormPDEScript/advectionDiffusion1D/README.md

@@ -2,42 +2,4 @@
 
 ## Advection-Diffusion with Gaussian Source
 
-This example demonstrates solving a one-dimensional advection-diffusion problem with a Gaussian source term using the FEAScript library. The problem models the transport equation:
-
-$$
-\frac{d^2u}{dx^2} - 10 \frac{du}{dx} = 10 \cdot e^{-200 \cdot (x - 0.5)^2}
-$$
-
-This can be written in the general form as:
-
-$$
-\frac{d}{dx}\left(A(x)\frac{du}{dx}\right) + B(x)\frac{du}{dx} + C(x)u = D(x)
-$$
-
-where:
-
-- $A(x) = 1$ (diffusion coefficient)
-- $B(x) = -10$ (advection coefficient)
-- $C(x) = 0$ (no reaction term)
-- $D(x) = 10 \cdot e^{-200 \cdot (x - 0.5)^2}$ (Gaussian source term centered at x = 0.5)
-
-### Instructions
-
-This example requires the `feascript` npm package and its peer dependencies (`mathjs`). It imports FEAScript directly from the npm package and runs the simulation in a Node.js environment. To run the example, follow these instructions:
-
-1. **Create package.json with ES module support:**
-
-   ```bash
-   echo '{"type":"module"}' > package.json
-   ```
-
-2. **Install dependencies:**
-
-   ```bash
-   npm install feascript mathjs
-   ```
-
-3. **Run the example:**
-   ```bash
-   node advectionDiffusion1D.js
-   ```
+This example demonstrates solving a one-dimensional advection-diffusion problem with a Gaussian source term. The problem models the transport of a substance under the effects of both diffusion and advection. For detailed information on the model setup refer to the corresponding [tutorial](https://feascript.com/tutorials/advection-diffusion-1d.html) in the FEAScript website.

examples/heatConductionScript/README.md

@@ -8,19 +8,19 @@ This directory contains Node.js examples demonstrating how to use the FEAScript
 
 #### 1. Heat Conduction Through a Wall
 
-This example demonstrates a heat flow case through a building wall. For detailed information on the model setup refer to the corresponding [tutorial](https://feascript.com/tutorials/HeatConduction1DWall.html) in the FEAScript website.
+This example demonstrates a heat flow case through a building wall. For detailed information on the model setup refer to the corresponding [tutorial](https://feascript.com/tutorials/heat-conduction-1d-wall.html) in the FEAScript website.
 
 #### 2. Heat Conduction in a 2D Fin
 
-This example demonstrates a typical cooling fin scenario. There are two Node.js implementations:
+This example demonstrates a typical cooling fin scenario. For detailed information on the model setup refer to the corresponding [tutorial](https://feascript.com/tutorials/heat-conduction-2d-fin.html) in the FEAScript website. There are two Node.js implementations:
 
 #### i. Standard Version (`heatConduction2DFin.js`)
 
 Basic implementation using the FEAScriptModel class
 
 #### ii. Gmsh Version (`heatConduction2DFinGmsh.js`)
 
-Implementation using an unstructured mesh generated by [Gmsh](https://gmsh.info/) (the mesh file, `rect_quad_unstruct.msh`, is also located in the current directory). For detailed information on the model setup refer to the corresponding [tutorial](https://feascript.com/tutorials/HeatConduction2DFin.html) in the FEAScript website.
+Implementation using an unstructured mesh generated by [Gmsh](https://gmsh.info/) (the mesh file, `rect_quad_unstruct.msh`, is also located in the current directory).
 
 ## Running the Examples