By 1864, Robert E. Lee's Army of Northern Virginia could no longer engage in the type of spectacular, rapid movements that brought battlefield success, albeit at high casualties. In the Overland Campaign, Lee was more willing to create fortifications that could be defended against superior U.S. Army numbers. The best examples of this are at Spotsylvania Court House, Cold Harbor, and Petersburg.

At Spotsylvania Court House, Lee's army formed a massive horse shoe shaped defensive entrenchment that enabled them to defend for days against repeated Union assaults. At Cold Harbor, entrenchments offered Confederates cover and enabled them to exact extremely high casualties from a force attacking over open ground. Lastly, at Petersburg, a full on siege with big guns, trenches, and a no-man's-land in between these entrenchment and Union lines is the most vivid parallel to the stagnation of trench warfare in the First World War.

Unfortunately, I do not have any citations for direct comparisons. However, Gary Gallagher's The Confederate War, and Lee and His Lieutenant's make some comments about Confederate strategy and change. As does Joseph Dawson, III and his debate on the Confederate Offensive-Defensive Strategy.

Hope that helps