In courts, government tribunals and regulatory agencies around world, Apple Inc. has argued that Samsung’s Android-based phones copy vital iPhone features. Samsung Electronics Co. is fighting back with its own complaints that some key Apple patents are invalid and Apple has also copied Samsung’s technology.

The two have each won and lost legal skirmishes over the last couple of years, and the companies appear oceans apart in settling their differences. Analysts predict continued litigation for months to come.

On Tuesday, the latest chapter opens in a federal courtroom in San Jose, where lawyers from the two companies and U.S. District Judge Lucy Koh will begin picking a jury to calculate how much South Korea-based Samsung owes Apple for infringing Apple’s patents on 13 older Samsung smartphones and computer tablets.

Representatives of both companies declined to comment.

A different jury in August found that Samsung infringed six Apple patents to create and market 26 smartphones and computer tablets. The panel ordered Samsung to pay Apple $1.05 billion.With Apple’s Cupertino headquarters about a 10-minute drive from the courthouse, potential jurors will be asked if any family members work for Apple and whether the company’s proximity will have any effect on their views of the case.

Koh then tossed out $450 million of that amount after deciding the jury wrongly calculated damages for 14 products. Amid an avalanche of legal filings afterward, Koh reduced the damages at issue to $400 million and the products to 13, then ordered a new jury to recalculate damages for those products.

Some four dozen people are listed on the trial’s witness list, many of them experts hired by Apple and Samsung to deliver damage estimates, which range from zero to more than the original $400 million.

Despite the amount of money involved, the current proceedings are somewhat of a warm-up for a much larger trial scheduled for March. That trial will focus on newer products still on the market, while the current trial is a battle over products that are several years old and no longer sold in the U.S. More money is at stake, and Apple is asking that Samsung be barred from selling some of its current devices in the U.S.

In both cases, jurors will hear from experts opining on the global market and offering dramatically differing views on damages. In the current case, the jury will determine damages by deciding — among other issues — whether Samsung’s behavior actually cost Apple sales.

Whatever the outcome, appeals are expected.

“This trial is just about money. Though several hundred million dollars are at stake, that isn’t going to make or break either of the companies involved,” said Mark Lemley a Stanford University law school professor who specializes in technology issues. “But the trial is also the last step in getting this case ready for the inevitable appeal. … That appeal will have broader ramifications.”

Apple transformed the mobile phone industry when it started selling the iPhone in 2007, but its success was quickly imitated and Samsung’s smartphone shipments surpassed Apple’s iPhone sales in 2011.

According to research group IDC, Samsung shipped 81 million devices in the July-to-September quarter for a market share of 31 percent, making it the world’s top seller. Apple is a distant second, having shipped 34 million iPhones, for a market share of 13 percent over the same period.